Entropy - Science topic

Hi Soumendra, quite interesting your analysis. Remember that time dilation goes together with length contraction so their quotient remains constant (speed C) and, most importantly, inertia increments with energy tested in the accelerators (m = E/C^2).

I agree that the traditional way of interpreting time dilation is inexact. Time does not get slow, the passage of time is universal! Special Relativity questioned this universality but since General relativity, it came hiddenly back.

General relativity deals with absolute concepts. Gravity is absolute and does not depend on the observer's inertial reference frame. Einstein´s equation is invariant under Lorentz´s transformation (mathematically the same as the previous sentence). Gravity is an effect of the presence of energy and energy is absolutely the same, it is invariant under Lorentz´s transformation. By this, time dilation and length contraction are also invariant under Lorentz´s transformation. But be careful, it is Total energy and not the kinetic component alone! This means that when energy is evaluated, besides kinetic energy, it must include mass energy, electromagnetic energy, and the energy from the strong-weak forces.

Returning to time, it does not slow down, because it will arrive to contradictions at speed C. This idea of the handle of the clock being stopped is conducted to think that photons are at all times and everywhere (time dilation to zero length). A better way to interpret the Lorentz gamma factor is to change scales! Attached is a drawing of how to understand time and length variations. Also, I´m attaching a paper about how to understand special relativity. I hope they will inspire in your research, regards

Dear Shabnam Naghshara ,

Any physical system cannot have zero entropy.

Even as its temperature approaches absolute zero. Indeed, this would mean that all components of the system have become identical. And this cannot be.

For a system with one single state, the entropy will be proportional to ln 1. That is, equal to 0.

Dear Sandeep Jaiswal and Harri Shore

Thank you both for your constructive comments. And, Sandeep, thank you for your clever rendition of the lines from The Rubaiyt of Omar Khayyam.

I have no doubt that you are sincere in your dedication to your research on time reversal, Sandeep, but I fear that your introduction of spirituality into the mix distracts from the credibility of your science. Science and spirituality tend to make uncomfortable bedfellows, at best.

You wrote: "To contemporary physicists, this may seem like an unattainable science beyond science, but ancient civilizations, particularly in India, mastered these principles long before they were relegated to mythology." With all due respect, however, if ancient civilizations had mastered these principles, why did they not use them to turn our world into an eternal paradise? Sadly, I fear that the world we see now falls far short of what many of us would consider to be a paradise.

In case you may not be aware of it, there is another discussion group at ResearchGate that goes by the title "Can philosophy help to innovate and develop scientific theory?" I can't help wondering whether your mix of science and spirituality might find a more comfortable fit on that discussion group? Regardless, I wish you well with your work on time reversal.

Best Regards,

JCNS

...the very words you use ('large heat source') contradict what you say. There's a third very definite equation that stands behind it.

I think the most suitable method to calculate total density of alloy is weighted average of the theoretical unit cell method

ρcomposite​=∑​(wi​⋅ρi​) 1

ρcomposite​: Total composite density (in g/cm³), wi​: Mass fraction of all phase and ρi​: Density of all phase (in g/cm³). First you need to Find phase ratio of all phases, you can find it by different techniques Such as refined SXRD data. Then you need to calculate density of each phase using Theoretical Density (ρ) as given below,

ρphase1=​z⋅M/ Vcell​⋅NA 2

here, z: Number of formula units per unit cell (depends on the crystal structure).M: Molar mass of the phase (g/mol), calculated based on its chemical formula , Vcell​: Volume of the unit cell (in cm³) and NA​: Avogadro’s number (6.022×1023 mol−1)

A LaFe11.64Si1.36 compound contain two phase one is NaZn13 other is LaFeSi

NaZn₁₃-type phase mass concentration = 19%

wNaZn13​=19/100​=0.19

LaFeSi type phase mass concentration = 100−19=81%

wLaFeSi​=81/100​=0.81

Calculate density using Theoretical Density (ρ) as given above,

you need z,M and Vcell,

Z=Total atom in unit cell/atom per formula unit

like NaZn13 phase has 112/14= 8

M=MLa+11.64.MFe+1.63Msi

M= 827.06g/mol

Vcell, you also find it form SXRD refinement or other techniques

Vcell=1051x10-21cm3

all values put into equation 2

ρ=8×827.06 / 1.51×10−21⋅6.022×1023​

ρphase1= 7.28g/cm3

Second Phase Similar,

such as LaFeSi phase calculated density using equation 2 given blew

ρphase1= 6.10g/cm3

Now use equation 1

7.28 ×0.19+0.81 ×6.1

= 6.324 g/cm3

This is the accurate density of total compound conation different phases

Sorry, actually the suggested pdf refers to a random variable that is the square of the inverse gamma distribution, so of course its entropy is finite.

Now let's discuss the relationship between Carnot efficiency and working fluid. Don't interfere with this issue by bringing downstream problems (be careful not to digress).

Carnot efficiency is not related to the working fluid, which means that the physical concept (Carnot efficiency) is detached from the physical entity (working fluid). The second law of thermodynamics cannot violate common sense. This mistake is that subsequent calculations of thermal work based on the second law of thermodynamics are also incorrect.

Even though it may not look like that to you, the calculations are actually based on the definition.

Now, about your proposed formulae: while in coarse, semiclassical approximation the internal energy could sort of be calculated in the proposed one-particle manner, in reality it is quantum mechanical and you can no longer simply break it down like that.

The entropy is an even bigger fish here: it cannot be divided into "one-particle contributions" like that, it has to be calculated via a partition function or something equivalent according to the quasi ergodic hypothesis (mean value over time = ensemble mean value).

Once you start calculating a partition function (or an equivalent) for the entropy, you get the internal energy "on the fly", so it makes no sense to use coarse approximations here, anyway.

It's a bit illogical, I won't argue anymore. Carnot efficiency is independent of the working fluid -—— the second law of thermodynamics violates common sense and is lower than the average level of human intelligence.

You have been given the original formulations by the original authors of the second law and a logical deduction above. If your textbooks convert this into an odd quantitative statement, their authors or translators did a bad job.

The actual second law is, as shown in my previous post, a pretty basic statement, so what you are fighting against has actually never been the second law. i get that after all the time you wasted on this that is hard to grasp.

The quantified threshold (not prediction) of the second law with respect to the Carnot cycle is:

"Es gibt keine Wärmekraftmaschine, die bei gegebenen mittleren Temperaturen der Wärmezufuhr und Wärmeabfuhr einen höheren Wirkungsgrad hat als den aus diesen Temperaturen gebildeten Carnot-Wirkungsgrad."

There is no heat engine, which at given mean temperatures of of heat input and output provides a higher efficiency than the Carnot efficiency calculated from these temperatures.

Science speaks in mathematics, and to prove the correctness of the second law of thermodynamics, quantitative predictions must be made and consistent with experiments.

Only some misunderstanding of the 2nd law of thermodynamics can cause any paradox.

It simply states that any change of state of any stable system requires an expenditure of some amount of energy to account for the change.

Bo Miao The reason for the entropy increase of closed systems, in apparent conflict with the unitarity of Hamiltonian evolutions (preserving information) is the lack of information (relevant entropy) of macroscopic observers [1]. The interpretation of the second principle and the flow of time as illusions [2] amounts to a realist interpretation of physics in a deterministic universe endowed with objective laws and properties, denying the central role of the macroscopic observer and its only intersubjective macroscopic observables.

So, the thermodynamical statistical grid of reading of macroscopic observers (living beings) is the basis of irreversible evolutions, second principle of thermodynamics, irreversibility and indeterminism of quantum measurements and existence of traces of the past...

...hence of any information allowing us to ascribe physical laws and properties to the universe.

You will find more references concerning entropy, the second law of thermodynamics and the flow of time in the.

[1] , Am. J. Phys. 67, 1078 (1999)

[2] "The distinction between the past, present and future is only a stubbornly persistent illusion". Einstein, 1955, in a condolence letter to the family of his best friend and collaborator Michele Besso.

I think that you arenot familiar with the fact that entropy is always expressed as negative delta S, -∆S. Absorption is "less negative", meaning approaching zero from a negative value, is a Decrease in practical entropy, albeit the number appears larger.

For example initial = -5S, after absorption = -1S. this is less entropy, moving toward zero, but expressed as -1 > -5

its the negative sign that throws everybody.

Your question can have a sens for a system at T=zero Kelvin. A molecule at this temperature don't oscillate but can spin in three sens or much more for a Universe with D-spatial dimensions.

Thank you. Your answers clearly demonstrate your level of discussion.

Q=f (T) is the mathematical expression of "Carnot efficiency is only related to the temperature of the heat source". DQ=df (T) The second law of thermodynamics in mathematics (S) is derived from this and the definition of dQ cannot be changed arbitrarily.

In fact, the second law of thermodynamics changes the mathematical representation of dQ.

I have answered this question in your new post:

Bo Miao

Please have a look at the JANAF Thermochemical Tables. You fill find there entropies as a function of temperature tabulated for many substances. There is a lot of experimental research to this end. Do you mean that these all experiments are wrong? By the way, JANAF means Joint Army and Air Force, as this tables have been created to help to compute the rocket propulsion. Try to do it without the Second Law.

Shen Wei Chen

Lyudmil Antonov

Dear Dr. Shen Wei Chen,

You preface your deliberations containing no definite and plausible question (here I do agree with Dr. Antonov to 100%!) as follows:

'In the realm of physics, the relationship between quantum mechanics and thermodynamics has long posed a significant challenge. The Many-Worlds Interpretation (MWI) offers a fresh perspective, allowing us to rethink the implications of quantum events and their potential connections to entropy'.

Howbeit, the Entropy Notion is IMPLICIT in QM via the mathematical formula S = k*ln(W), the well-known Boltzmann-Planck formula, expressing Entropy notion (S) via the Probability (W) of Lord Almighty knows what exactly.

Some 100 years ago, Erwin Schrödinger has taken this mathematical formula and simply replaced the letter W in it with the Greek letter Ψ to try clarifying the notorious Probability notion, whereas Entropy S he dubbed 'Mechanical Action'.

This is how, Hon. Prof. Schrödinger has used the physically correct picture of the Entropy notion in his seminal research paper (although the Entropy is but never the Mechanical Action as it is; instead, it ought to be a Summary Counteraction in regard to the relevant/pertinent non-zero Action).

The only step Hon. Prof. Schrödinger has but not come, to clarify the picture at hand to its conceptual end, was - and still is - the Probability (W) of Lord Almighty knows what exactly, which has become the Wave Function (Ψ) of some mysterious 'Probability Waves' - as Hon. Albert Einstein has perfectly & duly dubbed it).

Howbeit, it is exactly this step Hon. Prof. Dr. Schrödinger had conceptually missed to perform that was nonetheless successfully gone by one of 'Widely Unknown' thermodynamicists, Dr. Georg(e) Augustus Linhart, who could still have managed to completely decipher the magic W in the S = k*ln(W), with the help of proving that W = 1 + T/Tc, where T is the absolute temperature - and Tc to represent some characteristic temperature constant to duly define the pertinent temperature scale... Dr. Linhart has published his result in the well-known academic journal (JACS) some 100 years ago as well...

...To this end, Quantum Mechanics ought to be a valid and fruitful physical theory to correctly deal with the Intrinsically Soft Matter -> and rooted in or based upon the purely voluntaristic operational positivism -> but owing its final and undoubtedly seminal success to the Probability Theory - and/or the Mathematical Statistics, the old-and-good mathematical weapon against the Sheer Ignorance of whatever nature and from whatever source.

To sum up, above here, I have just mentioned my results of the exploration on the intersection between the quantum mechanics and thermodynamics, and I cannot share your enthusiasm that this "remains a promising area in contemporary physics research".

Nowadays, Quantum Mechanics has become old-and-good tool of the physical/chemical/biological mathematics, it does not need revisions and/or adjustments. We only do not need to confuse it with mathematical physics, chemistry, biology, etc...

Respectfully yours,

Dr. Evgeni B. Starikov

Hi Santanu, The following article discusses entropy calculation for subcooled flow boiling. I think you will get your answer from this article.

Wolfgang Konle ,

You said, "Inertia simply represents the capability of mass to store kinetic energy."

I agree with you.

I am comparing two objects with same mass and same kinetic energy that stay inert for different period of time.

Your "comprehensive" article is based on the same false assumption as this one. Read Planck's original book, it's free at Project Gutenberg and, as you said yourself, Germany in general and Planck in particular are the original sources, so he knows what assumptions he made. If you base your life on bad resources and don't want to see that, that's not the fault of my countrymen...

The question highlights the difference between how Carnot efficiency is studied in the second law of thermodynamics and how engineers approach practical thermal systems.

@Peter Enders Excuse me, i don't need your opinion i am seeking technical insight on it.

"Be more complete and logical." – Well, your statements are incomplete.

"Don't solve problems just because of a few trendy terms." – Well, please remember Clausis' famous statement about entropy (cf-, e.g., https://en.wikipedia.org/wiki/Clausius_theorem); it is an inequality, so one has to consider two different cases.

YOU started this discussion; I'm not here to do your homework.

Selecting the composition for Oxide Dispersion Strengthened (ODS) High Entropy Alloys (HEAs) involves several key considerations to optimize their unique properties. Here are some steps and factors to consider:

1. Element Selection

2. Phase Stability

3. Mechanical Properties

4. Thermal Stability

5. Corrosion and Oxidation Resistance

6. Processing Techniques

Example Composition

A typical ODS-HEA might include elements like Fe, Cr, Ni, Co, and Al, with Y2O3 as the oxide dispersant. The exact ratios would depend on the desired properties and application requirements.

References

For more detailed information, you can refer to recent studies and reviews on ODS-HEAs

Yes, differential entropy measures the uncertainty or randomness in a continuous probability distribution. It has physical meanings in:

Yes, differential entropy in continuous systems, such as pure jump Markov processes, does have physical and interpretative significance, though it differs from Shannon entropy in discrete systems. Here’s how differential entropy can be used to interpret continuous systems:

E is statistical to the same amount to which S is statistical, but since the trends in E can quite often be understood without explicitely invoking statistics, it is just skipped quite often in trend explanations.

E and S are both extensive quantities, so there is no spatiatemporal issue.

You are way too full of all kinds of misconceptions.

Start with a full intoductory physics

Series as the Berkly or Feyman.

I suggest to make DTA/DSC curve and to look where gamma prime dissolves, the temperature above is for solution treatment and where the gamma primes precipitates more readily during cooling, there or around for aging treatment. Little bit differs , if you aim for high creep strength or rupture strength.

Literature survey of silimar HESAs heat treatment would help too.

As multiple people have already informed you, your schematic has the error that the material independent efficiency is not a fixed value, but constitutes a maximum that you cannot overcome independent of the material, so the contradiction is non-existent.

But thanks for the new entertainment.

The blackbody cavity filled with CO₂ gas. This situation introduces additional complexities to the standard blackbody radiation model, which is typically based on an idealized cavity with no interactions with gases or other materials inside it. Here are some points to consider:

Blackbody Radiation and Planck's Law

Influence of CO₂ Gas in the Cavity

Modified Spectrum

Understanding the Deviation

My experience with ChatGPT (the paid version) was quite bad: it is impressive because it can now parse Word or pdf-texts, but it made a mess in interpreting my papers. It somehow always goes back to mainstream opinions on deep questions, and that does not help when you are working on something novel. Kindest regards - Jean Louis

yep. You can use vaspkit to output ZPE and entropy. But you first need to compute vibrational frequency (you can search setup in INCAR to calculate this one), then get freq from OUTCAR.

You are correct with your scepticism about the sometimes observed confusion between these terms in the context of HEAs and MEAs.

In metallurgy and generally in materials science, the stability of solid metallic solutions is governed by a complex interplay of thermodynamic factors when in equilibrium. Two key concepts in this context are configurational entropy (mixing entropy) and Gibbs free energy, which both indeed play crucial roles in stabilizing metallic solutions.

The configurational entropy, or mixing entropy, refers to the entropy change associated with the random arrangement of different atomic species in a solution, as described the partition function (Zustandssumme), i.e. the total multitude of states the atoms can be placed relative to each other. More of these possible arrangement lead to high mixing entropy. Essentially, this term thus quantifies the positional disorder introduced when different elements are mixed together in an alloy. For instance, in a binary alloy system with two elements, the configurational entropy increases as the atoms of these elements are mixed more randomly. The greater the randomness or disorder, the higher the entropy. This concept is indeed particularly significant in the formation of massive solid solutions high-entropy alloys (HEAs and MEAs), which are characterized by having multiple principal elements mixed in nearly equal proportions (in its original definition, which however is not always pertinent), resulting in an assumed high configurational entropy.

In stark contrast the term Gibbs free energy is a thermodynamic potential form that measures the maximum reversible work a system can perform at constant temperature and pressure. It serves as a comprehensive indicator of a system's stability, where a process or reaction is spontaneous if it leads to a decrease in Gibbs free energy. In metallic solutions, the free energy of mixing combines contributions from both enthalpy AND entropy to determine the overall stability of a material (i.e. it is inded NOT the entropy but Delta G that matters). The interplay between these factors dictates whether the alloy will form a stable solution or separate into different phases.

The stability of solid metallic solutions thus hinges ONLY on minimizing Gibbs free energy (all in equilibrium of course). High configurational entropy is only one of the factors that can promote stability by increasing the disorder within the alloy, thereby reducing the free energy. This reduction is crucial for maintaining a stable solution, especially in alloys with multiple elements. However, the enthalpy of mixing also plays a significant role as you correctly elude to. The enthalpy of mixing is the heat absorbed or released when different atoms mix (related to their bond strength). If the interactions between unlike atoms (those of different elements) are more favorable than those between like atoms (those of the same element), the enthalpy of mixing is negative, further stabilizing the solution by lowering Gibbs free energy. Conversely, if the interactions between unlike atoms are less favorable, the enthalpy of mixing is positive, potentially destabilizing the solution by increasing Gibbs free energy.

You are therefore indeed correct that enthalpy contributions also significantly affect the phase behavior and stability of metallic alloys. Depending on whether the enthalpy of mixing is positive or negative, various scenarios can arise. If the enthalpy of mixing is negative and sufficiently large, the alloy forms a completely miscible solid solution across all compositions, as the attractive interactions between different atoms dominate. A small positive enthalpy of mixing can result in partial solubility, where the alloy exhibits miscibility gaps, leading to phase separation at certain compositions and temperatures. A large positive enthalpy of mixing leads to immiscibility, causing the elements to segregate and form distinct phases rather than a solid solution. Additionally, alloys can exhibit ordered structures at lower temperatures and disordered solid solutions at higher temperatures. This transition is driven by the competition between the enthalpic preference for ordering and the entropic gain from disordering.

It must also be noted (and s sometimes overlooked in this field) that - apart from configurational entropy terms - also other types of entropy can influence the stability of metallic solutions. Vibrational entropy, associated with atomic vibrations in the lattice (use e g Debye theory), increases with temperature and can affect phase stability. High vibrational entropy can stabilize certain phases at elevated temperatures. Electronic entropy arises from the distribution of electrons among energy levels. It is generally small compared to configurational and vibrational entropy but can be significant in materials with complex electronic structures. Magnetic entropy, relevant in alloys with magnetic elements, is related to the alignment of magnetic moments and can influence phase stability, particularly in magnetic transitions.

The stability of solid metallic solutions thus indeed results from the intricate balance between configurational entropy and Gibbs free energy, with significant contributions from enthalpy and other forms of entropy. High configurational entropy favors stability by increasing disorder and lowering free energy. The enthalpy of mixing, depending on its sign and magnitude, can either promote or hinder the formation of stable solutions. A thorough understanding of these thermodynamic principles is essential for designing advanced materials with desired properties and stability.

I attach some papers where I also tried to disentangle these contributions a bit, trying to show that the design of HEAs (and related) is indeed NOT a single facetted (mixing entropy-focussed) thermodynamic task.

Good luck!

Bo Miao

The concept of perpetual motion machines has fascinated scientists and inventors for centuries. However, it’s essential to understand that true perpetual motion machines are impossible due to the laws of thermodynamics. Let’s break down the scenario you’ve described and address the researcher’s question.

A perpetual motion machine is a hypothetical device that can perform work indefinitely without an external energy source. Such a machine would violate the laws of thermodynamics. The laws of thermodynamics apply universally, regardless of the system’s size or complexity. There are three types of perpetual motion machines:

Machines of the First Kind: These machines produce work without any energy input. They violate the first law of thermodynamics. Machines of the Second Kind: These machines spontaneously convert thermal energy into mechanical work without any input. While they don’t violate the conservation of energy, they do violate the second law of thermodynamics. Machines of the Third Kind: These machines continue to be in motion forever due to inertia, but they cannot exist in practice due to unavoidable dissipation (e.g., friction).

In your scenario, you have two containers (A and B) separated by a transparent solid. Container A contains CO2 at a concentration of 3 mol/L, while container B contains CO2 at 1 mol/L. Radiation energy is transferred from container A to container B. The temperature in container B (Tb) is higher than in container A (Ta).

You are interested in whether this setup could lead to a perpetual motion machine based on radiation. Unfortunately, this scenario does not solve the problem of perpetual motion. Here’s why:While radiation is a long-range interaction, it still obeys the laws of thermodynamics.

The second law of thermodynamics states that the entropy (disorder) of an isolated system tends to increase over time. In other words, energy spontaneously flows from hotter regions to cooler regions. In your setup, container A (with higher concentration) will naturally radiate energy to container B (with lower concentration), resulting in cooling of container A. This process cannot continue indefinitely without an external energy source.

The temperature difference (Tb > Ta) does not change this fundamental limitation.

Even if you were to achieve perfect control over radiation, the energy stored in the CO2 concentrations would eventually be exhausted. Perpetual motion machines remain theoretical and cannot be commercialized because they violate the laws of thermodynamics.

In summary, while the concept of using radiation for energy transfer is intriguing, it does not provide a solution to perpetual motion. Researchers should focus on practical and sustainable energy solutions that adhere to the fundamental principles of physics

Everyone can compare and read to see who is bragging.

Hi Sai Yagnamurthy,

Pls, check this one.

Regards

G

The second law of thermodynamics is a fundamental principle in physics that describes the direction of natural processes and sets limitations on the efficiency of heat engines. It can be stated in various forms, but one common statement is that in any spontaneous process, the total entropy of a closed system plus its surroundings will increase.

While the second law has been extraordinarily successful in explaining and predicting the behavior of systems, it's worth noting that there can be challenges in applying it universally to every situation, particularly at the microscopic level or in systems that are far from equilibrium.

One reason for potential inconsistencies with experiments could be the difficulty in precisely defining and measuring quantities like entropy, especially in systems with many particles or complex interactions. Entropy is a measure of the disorder or randomness of a system, and its calculation often relies on statistical mechanics, which involves making statistical assumptions about the behavior of particles.

Additionally, at the microscopic level, there are instances where the behavior of individual particles may seem to violate the second law, leading to discussions about statistical fluctuations and the arrow of time. However, these apparent violations typically occur on very short timescales or involve very small systems and do not contradict the overall validity of the second law for macroscopic systems.

As for symmetry and conservation, the second law doesn't strictly require these properties. Symmetry and conservation principles are important in physics, but the second law is more about the directionality of processes rather than symmetries or conservations.

Overall, while the second law of thermodynamics has been extremely successful in describing the behavior of macroscopic systems, there are still ongoing debates and research efforts to understand its implications at smaller scales or in more complex systems. These discussions often lead to deeper insights into the nature of thermodynamics and the behavior of physical systems.

Dear Arieh,

Thank you for your insightful response and for highlighting the importance of context when discussing entropy. Your point about entropy being a state function, determined for a macro-system at equilibrium, is well taken. I appreciate the opportunity to further clarify and expand on my position regarding entropy and the Arrow of Time.

You are absolutely correct that entropy is a state function, meaning its value depends on the state of the system and not on the path taken to reach that state. This foundational concept is crucial in thermodynamics and helps avoid misunderstandings about entropy’s behaviour.

I agree that it is essential to specify the system and the process when discussing whether entropy increases. Traditional thermodynamics tells us that for isolated systems, entropy tends to increase, leading to the Second Law of Thermodynamics. However, recent research by me, including the study I referenced by myself, challenges this view by suggesting scenarios where entropy remains constant, particularly in non-isolated systems or when considering quantum effects.

The latest research I mentioned posits that under certain conditions, entropy does not necessarily increase and could be constant. This assertion arises from the exploration of systems beyond the classical isolated frameworks typically considered. The implications of these findings are profound, potentially altering our understanding of thermodynamic processes, particularly in complex or quantum systems.

Regarding the Arrow of Time, the traditional view holds that it aligns with the increase of entropy, thus giving time a direction from past to future. However, the concept of T-symmetry (time-reversal symmetry) suggests that the fundamental laws of physics should remain invariant if time were reversed. The new findings propose that if entropy can be constant, then the Arrow of Time might be T-symmetric, challenging our conventional understanding and opening new avenues for theoretical exploration.

I would love to delve deeper into the specifics of the system and processes under which these new entropy findings were derived. Perhaps we can examine particular case studies or models where entropy behaves differently than traditionally expected. This could lead to a richer understanding of both entropy and the Arrow of Time.

Thank you again for your thought-provoking response. I look forward to continuing this stimulating discussion and exploring these groundbreaking ideas further.

Best regards,

Sandeep

Solution to this one:

So once more you have shown that if you violate the first law, you also violate the second law.

way to GPT4 Rho dot Rho. i was already familiar, with some of these pieces, i am looking for refrences please and thank you.

The second law of thermodynamics contradicts itself. Scientists are also addicted to the surface of experience.

Galileo's introduction of Aristotle's theory of falling is contradictory, and Aristotle's theory of falling is ineffective.

Lucas Lima

Your case is similar to the thermodynamics of the dissolution of hydrocarbons in water. This is due to quantum phenomena in the process. In some cases, it is impossible to formulate a theory of thermodynamics without the concept of a microstate. Microstates are best understood in terms of quantum states S = − Tr ρ log ρ , where Tr -trace, ρ is the density matrix. In linear algebra trace square matrix A, denoted tr(A). You calculated thermodynamics within the framework of classical thermodynamics. It is necessary to take into account quantum phenomena.

The studies related to irradiation are mentioned in this review article:

https://iopscience.iop.org/article/10.1088/1402-4896/ad1d3e/meta

Dear Bo Miao ,

I understand your concern, as at first glance, it seems like there are more equations than variables, which could imply that there is no solution. However, upon a more rigorous mathematical analysis, I believe the second law still holds in this case.

In your system, you have CO, O2, CO2 gases, and solid carbon (C) with three chemical equilibrium reactions: 2CO + O2 ⇌ CO2, C + O2 ⇌ CO2, and C + CO2 ⇌ 2CO. The corresponding equilibrium equations are ρ_co^2 / (ρ_co2 * ρ_o2) = K1, ρ_co2 / ρ_o2 = K2, and ρ_co^2 / ρ_co2 = K3. Additionally, you have an element conservation equation, 0.5ρ_co + ρ_co2 + ρ_o2 = A, where A is the average concentration of O2.

The equilibrium constants K1, K2, and K3 are not independent variables. They are related to the Gibbs free energy change (ΔG) of each reaction at a given temperature T by the equation ΔG = -RT ln(K), where R is the gas constant. Therefore, only two of the three K values are independent.

We can rewrite the equilibrium equations in terms of ΔG: ΔG1 = -RT ln(K1) = -RT ln(ρ_co^2 / (ρ_co2 * ρ_o2)), ΔG2 = -RT ln(K2) = -RT ln(ρ_co2 / ρ_o2), and ΔG3 = -RT ln(K3) = -RT ln(ρ_co^2 / ρ_co2). The sum of the ΔG values for the three reactions must be zero, as the overall process is at equilibrium: ΔG1 + ΔG2 + ΔG3 = 0. Substituting the expressions for ΔG1, ΔG2, and ΔG3, we get -RT ln(ρ_co^2 / (ρ_co2 * ρ_o2)) - RT ln(ρ_co2 / ρ_o2) - RT ln(ρ_co^2 / ρ_co2) = 0.

This equation, along with the element conservation equation, forms a system of two equations with three variables (ρ_co, ρ_co2, ρ_o2). While this system is underdetermined, it does not necessarily mean there is no solution or that the second law of thermodynamics is violated. The second law states that the entropy of an isolated system at equilibrium is maximum, and the change in Gibbs free energy is zero. The equilibrium state of this system, if it exists, would satisfy these conditions.

The apparent contradiction between the number of equations and variables in this chemical system does not inherently violate the second law of thermodynamics. The equilibrium constants are related through the Gibbs free energy, reducing the number of independent equations. The system may have an equilibrium state consistent with the second law, even if it is not uniquely determined by the given equations alone. Additional constraints, such as the positivity of concentrations or the minimization of Gibbs free energy, could potentially lead to a unique solution.

The second law of thermodynamics is a fundamental principle that has been extensively verified experimentally. I think it is important to critically examine such principles, but the presented argument does not provide sufficient evidence to overturn this well-established law.

Best,

Alessandro Rizzo

So what is the problem? You obtain more than one solution; one of them has the lowest Gibbs energy (assuming that you keep the pressure and the temperature constant), and that is the stable state.

Changing the conditions, i.e., adding a mixture component, can eventually make the system jump to another stable state. This phenomenon has been described, for instance, for the ammonia synthesis from hydrogen and nitrogen.

There is no problem with the 2nd Law.

СПОСОБ ПОЛУЧЕНИЯ МНОГОКОМПОНЕНТНЫХ ПОКРЫТИЙ ИЗ ЦВЕТНЫХ МЕТАЛЛОВ Князьков А.Ф., Князьков С.А., Гаврилин А.Н., Дитенберг И.А., Гриняев К.В., Смирнов И.В. Патент на изобретение RU 2690265 C1, 31.05.2019. Заявка № 2018123837 от 02.07.2018.

СТРУКТУРА И СВОЙСТВА МНОГОКОМПОНЕНТНОЙ НАПЛАВКИ НА СТАЛЬНОЙ ПОДЛОЖКЕ, ПОЛУЧЕННОЙ ПУТЕМ ИМПУЛЬСНОЙ ПЕРЕПЛАВКИ ПОРОШКОВОЙ СМЕСИ W-CR-MO-ZR-TI-TA-NB-СU ЭЛЕКТРИЧЕСКОЙ ДУГОЙ С НЕПЛАВЯЩИМСЯ ЭЛЕКТРОДОМ В ЗАЩИТНОЙ СРЕДЕ АРГОНА Гриняев К.В., Смирнов И.В., Осипов Д.А., Дитенберг И.А., Князьков А.Ф., Князьков С.А., Гаврилин А.Н. В книге: Физическая мезомеханика. Материалы с многоуровневой иерархически организованной структурой и интеллектуальные производственные технологии. Тезисы международной конференции. Томск, 2021. С. 144.

КОНЦЕПЦИЯ ВИБРОЗАЩИТЫ ТЕХНОЛОГИЧЕСКОЙ СИСТЕМЫ ПО РЕЗУЛЬТАТАМ ВИБРОМОНИТОРИНГА ДЛЯ ЭФФЕКТИВНОЙ МЕХАНООБРАБОТКИ Гаврилин А.Н. автореферат диссертации на соискание ученой степени доктора технических наук / Национальный исследовательский Томский политехнический университет. Томск, 2022

High entropy alloys (HEAs) continue to be an exciting area of research with numerous potential applications across various industries. Here are some recent research topics and areas of investigation in the field of HEAs:

These research topics reflect the diverse range of opportunities for advancing the understanding and applications of high entropy alloys in materials science and engineering. Researchers continue to explore new avenues for optimizing the properties and performance of HEAs to meet the demands of modern technology and industry.

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From the second law of thermodynamics in an reversible process one has:

TdS=dU+p dV

where S is the entropy, T is the absolute temperature (in K), p the pressure and V the volume. For an ideal gas p=R T/V where R is the ideal gas constant. For an ideal gas the internal energy is only a function of temperature hence dU =Cv dT, where Cv is the specific heat at constant temperature. Also for an ideal gas R=Cp-Cv where Cp is the specific heat at constant pressure. Hence the second law of thermodynamics combined with the first law becomes:

dS/Cv=(dT/T)+ (R/Cv)(dV/V)

For an isothermal process dT=0 so that a compression dV/V<0 implies a reduction of entropy. For a gas with constant Cv one can furthermore write:

(S-So)/Cv=ln(T/To)+(R/Cv)ln(V/Vo)

and

R/Cv=gamma-1

Sonlu ve sonsuz yaklaşımlarda amaç var olan bir netice elde etmektir ve sonucun doğruluk payı önemli. Yaklaşımın ne kadar uzun olduğu önemli değil.

The formula change in S = dQ/T refers to a particular case, that of simple thermal heating. The expansion of an ideal gas into a vacuum involves no change in energy, so this formula does not apply to that case.

Bo Miao

i assume this is genuine question you have raised;

leading with that,

The statement that gas radiation and absorption could invalidate the Second Law of Thermodynamics is a misunderstanding of how thermodynamics and heat transfer operate. The Second Law of Thermodynamics, in its simplest form, states that in any closed system, the entropy (a measure of disorder or randomness) tends to increase over time unless energy is put into the system to maintain or decrease entropy. This law is one of the fundamental principles underlying much of physics and engineering and is observed to hold true in countless experimentation.

Regarding the specific points raised:

1. Gas Radiation and Absorption

it true that gases at different locations can absorb radiation differently and this can lead to temperature differences across a system. However, this process does not violate the Second Law of Thermodynamics. The law does not imply that temperature differences cannot exist or that they cannot change; it primarily concerns the overall entropy of a closed system. In the context of gas radiation, the energy transfer through radiation leads to changes in temperature and can drive processes that increase the system's overall entropy.

2. Temperature Differences and Entropy

The creation of temperature differences through radiation absorption and emission is a part of how heat transfer operates in the universe. These processes, including conduction, convection, and radiation, are mechanisms for energy distribution and do not inherently contradict the Second Law. The entropy increase or decrease in a particular part of a system does not imply a violation of the law as long as the total entropy of the closed system, when considering all interactions, does not decrease.

3. Perpetual Motion Machines

The idea of a perpetual motion machine—a machine that can operate indefinitely without an energy source—is a concept that violates the First and/or Second Law of Thermodynamics. Despite extensive theoretical and experimental exploration, no such machine has been created or observed to exist. The Second Law, among other principles, indicates why perpetual motion machines are not feasible.

I did struggle to understand the non sequiator in your comments, as per the suggestion that belief in such devices is contingent on catastrophic events like nuclear war…it is not grounded in scientific reasoning.

Scientists rely on empirical evidence and theoretical consistency to validate or refute theories. The Second Law of Thermodynamics is supported by a vast body of evidence and theoretical understanding, making it one of the cornerstones of physical science. While scientific understanding evolves with new discoveries, any new theory or observation that appears to contradict well-established laws like the Second Law of Thermodynamics requires rigorous scrutiny, experimental validation, and theoretical explanation within the broader framework of physics.

best

H

Three formulas can explain that gas radiation cannot reach thermal equilibrium, and the second law of thermodynamics is incorrect.

L.D. Edmonds All measurement "devices" collapse quantum wavefunctions by putting the quantum system that is being measured in contact with the "devices" thermal bath. The quick answer to your question is the thermal bath entropy of any measurement "device."

Metal tozlarının yüzdesi birbirine en yakın olan alaşım seçilir.

That's not a consequence of the 2nd law of thermodynamics, that's simply the symmetry of second derivatives [also known as Schwarz theorem, Clairaut theorem or Young theorem] which is valid for any mathematical function of state. By this method, the extremely useful Maxwell relations can be derived for a single system.

No mathematical or physical overdefinition issues observed here.