Science topics: Physical SciencesThermodynamics

Science topic

# Thermodynamics - Science topic

Thermodynamics is the branch of natural science concerned with heat and its relation to other forms of energy and work.

Questions related to Thermodynamics

If one uses a coordinate transformation, say t -> a t' +b_i x^i, does it change the thermodynamic quantities of a black hole, say entropy, temperature and others?

the general question is that: does coordinate transformation change the Smarr relation (the generalized form of the first law of black hole thermodynamics)?

Can absorption isotherms be used for gas-liquid absorption processes?

Hi all,

To set things clearly: I am a PhD student working on the process implications of electryfing the ammonia production by replacing conventional SMR with Water Electrolysis. A part of my preliminary work is to assess the difference in theoretical minimum energy consumption. To do so, I have calculated a first approximation by summing up the reactions (SMR, Water gas shift, Haber-Bosch,...) and calculating the enthalpy of the resulting "total" reaction. I have done this for the "Water Electrolysis + Haber-Bosch scenario" and validated the minimum with values from the literature.

However, for the conventional "SMR + Haber-Bosch scenario", values from the literature are different. To be more specific, here is the energy minimum calculated in the following conference paper:

*(...) the theoretical minimum of energy consumption for the process itself (represented by LHV of methane) is 22.2 GJ/t NH3 (...)*

Conference Paper 2. Kirova-Yordanova Z, Energy Integration and Cogeneration i...

So here is my question: Why use the LHV of methane (instead the enthalpy of reactions) to calculate the energy minimum ? I feel like this is incorrect as I do not take into account the synthesis of methane.

Thanks in advance for any answers,

Antoine

One might argue: Animals increase their survivability by increasing the degrees of freedom available to them in interacting with their environment and other members of their species.

Right, wrong, or in between? Your views?

Are there articles discussing this?

Can absorption isotherms be used for gas-liquid absorption processes?

Looking for information on Microscopic Thermodynamics? Check out this repository of information and examples made available free on the Web by Professor Pohl, derived from his classic textbook,

*Microscopic Thermodynamics*, by Irey, Ansari and Pohl, John Wiley and Sons, 1976, ISBN 0-471-42847-7. http://thermospokenhere.altervista.org/Hello,

I have a vapor production device that provides me with air+steam flow of 80% or 40% w/w (volume ratio) water vapor quality at 100 degC. The flow passes through a series of valves and tubes where it cools down because of heat transfer. There, the temperature is measured to be something around 50deC. I know that at 50degC, this amount of water vapor corresponds to super-saturated flow. So, I assume that the extra water vapor has been condensed inside the tube, and the resulting flow is a saturated vapor (I don't have access to see how much water has been condensed). Do you find this assumption realistic? Or I may be dealing with a super-saturated flow?

On the other hand, I am a bit uncertain about the measurements of the temperature sensor. To what extent, do you think that latent heat of condensation on the sensor can affect the temperature reading?

Is that right? (From an article,

*Using graph theory to analyze biological networks.)*Things flow in biological systems: energy, nutrients, blood, air, as examples.

A graph is a set of points with connections.

A graph is like a photograph. Biological systems are like movies. If that analogy is valid (well, maybe it is not?), then graphs are not the optimal way to model biological system; it is necessary to also model flow.

Your views?

I would like to know how to calculate the thermal power in kWth. Is it possible to convert it to kW or kWh or J? is 1kWth equivalent to 1kW? Because kWth is an additional SI power unit, I base it on the attached material, but I need more information on how to convert it from other units. Maybe it is a very basic and easy question, but I would be very grateful for any materials and explanations.

The general consensus about the brain and various neuroimaging studies suggest that brain states indicate variable entropy levels for different conditions. On the other hand, entropy is an increasing phenomenon in nature from the thermodynamical point of view and biological systems contradict this law for various reasons. This can be also thought of as the transformation of energy from one form to another. This situation makes me think about the possibility of the existence of distinct energy forms in the brain. Briefly, I would like to ask;

Could we find a representation for the different forms of energy rather than the classical power spectral approach? For example, useful energy, useless energy, reserved energy, and so on.

If you find my question ridiculous, please don't answer, I am just looking for some philosophical perspective on the nature of the brain.

Thanks in advance.

I want to study the interdiffusion of Ni/Ti bilayer at 500 degrees. I have relaxed the interface and calculated the interfacial energy. My next step is to do MD simulation. Should I need to convert my Ni/Ti crystal bilayer to amorphous Ni/Ti bilayer (by heating at quenching) and then use a thermodynamic ensemble to study the interfacial reaction and diffusion?

Lee's disc apparatus is designed to finsd thermal conductivity of bad conductors. But I am having a doubt that, since soil having the following properties:

1. consists of irregular shaped aggregates

2. Non uniform distribution of particles

3. Presence of voids

Can we use Lee's disc method find thermal conductivity of soil???

I'm going to work on a

**CHP system**and I'll need to simulate it to calculate energy, exergy, exergyeconomic, and exergoenvironmental parameters**(4E analysis)**. Previously, this was supposed to be done in**the****engineering equation solver (EES)**. But now, I'm looking for someone who has experience working with Thermoflow. Is it possible to calculate these parameters in Thermoflow?Actually, I'll need to make an optimization (from the perspective of thermodynamics and economic factors). Is this possible to achieve them in Thermoflow instead of EES??

*I'd appreciate your responses in advance.*

Dear Colleagues

I hope you are doing well. I want to calculate thermodynamic properties of ammonia and water mixture. A part of my simulation is shown below:

X=0.5294

Y=1-X

h = refpropm('h', 'T', 67.7+273.16, 'P', 116.92, 'water', 'ammonia', [Y X])

However, following error is shown:

Error using cell2mat (line 52)

CELL2MAT does not support cell arrays containing cell arrays or

objects.

Error in refpropm (line 318)

z_kg = cell2mat(varargin(nargin));

What should I do?

why emulsions are always thermodynamically unstable? how to solve this problem

A water-in-oil emulsion is prepared by homogenising 5 cm3 of water into 10 cm3 of dodecane containing surfactant. The average radius of the droplets is 12 m. Calculate the total oil-water interfacial area generated in the emulsion in SI units. State any assumptions you make.

**1, The gas diffuses to vacuum,dq = 0, dS = dQ / T = 0,so the entropy in the**

**diffusion process cannot be calculated: S (T1).**

2,

**If S (T1) has no physical meaning, then S (T0) and S (T1) have no physical****meaning.**

Good morning,

I would like to know if any of you has reviews or courses about this topic "isotopic exchange" ( Kinetics, Thermodynamics )?.

Thank you in advance!

Dear Colleagues,

I can't properly understand why VdP is not included in First Law of Thermodynamics.

If I add δQ amount of heat energy to a system, then some of this energy increases the internal energy U of the system. Internal energy means the kinetic energy of the gas particles ( For ideal Gas).

This is dU. Some part is used to do the external work. This is PdV. And some part is used to stored as pressure energy. This is VdP.

So, δQ = dU + PdV + VdP.

But VdP is not included in First law of thermodynamics.

Please help me to explain this confusion.

Thanks and Regards

N Das

I used CPMD (with PBC) to perform MD with constraints at different values of a reaction coordinate, and the resulting free-energy profile, obtained after thermodynamical integration, does not appear smooth. The barrier seems OK but the product region, at large values of the reaction coordinate, exhibits oscillations. What could cause such artifacts?

The science of energy and work and health is important in chemistry and physics ,but it deals with health as many factors like food ,diet and disease ,how this is affect the health?

Is there a computational or analytical method to calculate the corrosion resistance of a superalloy based on the composition of the alloy and thermodynamic parameters obtained by ThermoCalc?

Please, if anyone could clarify this question I received from one of the reviewers of my manuscript. What am I supposed to present?

"discuss the mechanism thermodynamically, where photo generated holes and electrons can be involved in the photocatalytic reaction."

are can some models thermodynamics is not given the correct coordination of plait point in ternary system?with know are given good results tie-lines calcul. regards

A very interesting topic, "quantification of randomness" in mathematics it is sometimes reffered to as "complex theory" (although it is more about pseudorandom than randomness) that is based on saying that a complicated series is more random and then there are tests for randomness in Statistics and perhaps the most intriguing test related to information theory -"entropy"(as also being of relevence to and result of second law of thermodynamics), while there are also random numbers generators (pseudorandom numbers generators) and true random numbers generators using quantum computing.

So, what I've been trying to, is making a complete list of all available algorithms or books or even random number generators that will allow me to tell me how much random a series is, allowing me to "quantify randomness".

There are 125 unique infinite series which are pseudorandom that I have discovered and generated based on a rule, now how do I test for randomness and quantify it? Uf the series is random or there is probably a pattern, or something that will allow me to predict the next number in the series given I don't know what the next number is.

Now, do anyone know of any github links based on any of the above? ^ (like anything related to quantifying randomness in general that you think will be helpful).

A book/books on quantifying randomness will be very very helpful too. Actually anything at all...

Theoretically speaking, when subsonic reactant flow passes through strong deflagration waves (strong expansion waves), the products must be in supersonic speed. But this is not possible because it violates the thermodynamics second law.

Can anyone please explain how?

Dear community,

I was modelling recently binary systems (such as 1-octanol/Nitrogen) at elevated pressure and temperature by PC-SAFT. The point where the bubble and dew point curves meet mark the mixture's critical point. Regarding a binary system the so called "critical locus" with different temperatures, pressures and compositions, connects the critical points of the pure components.

When determining the mixture's critical points (as shown in the attached figure) by PC-SAFT a sharp rise of bubble and dew point curves can be observed in the region where the mixture's critical point (for the regarded pressure) should be located.

Is there to your knowledge a physical reason for the observed phenomenon? Or is it solely to model inaccuraties in the range where the dew and bubble point curves merge?

With best and thanks in advance, Michael

Arrow of time (e.g. entropy's arrow of time): Why does time have a direction? Why did the universe have such low entropy in the past, and time correlates with the universal (but not local) increase in entropy, from the past and to the future, according to the second law of thermodynamics? Is this phenomenon justified by the Gibbs law and the irreversible process?

With respect to all the answers, in my opinion, no answer to such questions is completely correct.

The second law of thermodynamics violates the epistemology of "internal causes determine external manifestations".

From the picture (book content), the second law of thermodynamics deduces: "the efficiency of Carnot heat engine has nothing to do with the thermophysical properties of working medium". This is absurd, like "human looks have nothing to do with genes"

"Carnot heat engine efficiency and human appearance" belong to external appearance, while "working medium thermophysical properties and genes" are internal causes. Internal causes determine external appearance.

Thermologists over consume "anti perpetual motion machine" and "irreversible". The second law of thermodynamics violates the rigor of science.

As part of my project, I plan to model the

**water-ammonia adsorption refrigeration cycle**at**EES**. I acted according to the manual of EES, but unfortunately, I can not find the**MASSFRACTION**and**QUALITY**functions in the function info and in the Brines section. There is the ammonia-water mixture but the mentioned functions do not exist.I read the link mentioned at the end, but unfortunately, I could not find them in my software version.

Thank you in advance for your help.

It is interesting to note that there are analogies between economy and a thermodynamic framework. I have only begun to delve into this inter-connection. It looks like the thermodynamic analogy has not served very far. I have visited some lectures by Prof. Steve Keen. He emphasizes the importance of energy conversion in producing surplus in an economy. Labor and Capital are only means to achieve work from given resources. He is also of the view that macroeconomics can be formulated without any microscopic foundations. So that sounds thermodynamic, as a self-consistent framework, although we have a statistical foundations for thermodynamics. But also I am wondering if financial crises may be described as sort of phase transitions. And how to describe a stable economy as a steady state system? Any opinions or suggestions for interesting ideas, or the state of research in this direction, are welcome.

Since V changes with changing P and T in high pressure you cant simply get a P-T curve for constant V.

The rate of a chemical reaction is typically given by r = k[A][B] where [-] indicates concentration. However, it seems to make sense to use r = k{A}{B}, where {-} indicates activities, since the activity represents the effective concentration. I've found two papers that use this method for the hydration kinetics of carbon dioxide, with good results:

However, in the classic work on "Gas-liquid reactions", Danckwerts says the following:

"It is a mistake to suppose that, when the reactants are non-ideal solutes, thermodynamic activities should be substituted for concentrations in the rate-equation, and that the corresponding rate-constant will then be independent of composition. This formulation is misconceived in principle, and in practice the use of concentrations usually leads to somewhat better results that the use of activities"

I know the Danckwerts book is from 1970 and the papers above are from 2007 and 2010, but they knew their stuff back in the day! What has changed? Why is this formulation misconceived? And who is right?

Lastly, I know the rate equation is itself a simplification of the actual process, but if I want to get an accurate estimate, should I use concentrations or activities?

Statistical mechanics considering interaction is attached to the second law of thermodynamics. Considering the influence of temperature on the interaction potential, statistical mechanics can prove that the second law of thermodynamics is wrong.

I want to calculate thermodynamic properties, but in Gibbs2 calculations the temperature and pressure range selecte by default. I want to select it manually, please some one help me regarding my issue.

thank you.

Let's imagine a clean surface of stagnant

**Al-Mg-Ca**melt. We know that surface-active elements such as**Ca**and**Mg**have a higher concentration in the surface layer. During my investigations, I have found out that there is a possible "**lateral**" difference of the concentration at the outmost surface layers of the melt. Meaning, the concentration of the Ca atoms is higher at some points of the surface compared to the nearby regions on the surface. How can this lateral difference in the composition be explained?i need the solution of thermodynamics of hydrocarbon reservoirs by dr.firoozabadi .especially chapter 2 & 3.

I am looking for reasoned / reasonable explanations of the dynamic behavior of bulk and surface nanobubbles.

When depicting the melting curves of proteins, lots of DSC studies were done with samples containing molar-scale denaturants such as urea and GuHCl. However, if denaturants destroy the protein structure, shouldn't the experiments be focused on the native thermostability of proteins? Why can't native proteins be studied using DSC? I'm quite new to this area and would appreciate any opinions.

I need data on thermodynamic excess functions or vapour pressures or activity or activity coefficients of water - N-methylacetamide mixtures. I have searched but I can't find anything. Can someone give me a "hint".

Thank you very much and I hope you can help me.

Dr. Felipe Hernández-Luis

I am looking for appropriate research on the process of matching the turbocharger to marine diesel engines. If you know relevant references, books and articles in this field, I will appreciate introducing them to me. Thanks.

I am Looking for a Reaction or phase change material to Produce Heat From Ice to oprate the fuel cell in Sub-Zero temprature in Static conditon. to oprate AFC's it is needed to be heated up.

Hello, I've been investigating a bunch of monomers which spontaneously react in water to form a polymer. I would like to know how to calculate the thermodynamics of such a system. On the surface, this seems like a straight-forward question, however, I've only seen implementations of thermodynamic integration, free energy perturbation, or umbrella sampling for the most part. Unfortunately, my system is not simply A + A = B, it's A + A + A + A + A + A(n) = B(n). i.e. it's 10 monomers linking together to form a single polymeric molecule. Now in TI, FEP, or US most implementations are simply atom 1 of molecule A and atom 2 of molecule B are constraint and bonded/broken. However, for a many reaction system, how much one achieve Gibbs energy and entropy? I would ideally like to compare the Gibbs energy of state 1 (only monomers in solvent) and state 2 (polymer in solvent). And then also look at solvation energy by obtaining state 3 (only solvent). Is there a way to obtain JUST the thermodynamics of a single set of trajectories or from a single simulation? Why do we need to use two separate simulations which are compared? How would I obtain G and S for my hypothetical system?

Thank you!

The second law of thermodynamics violates the basic definition of thermodynamics

1. The physical definition of thermodynamic efficiency can get the opposite conclusion of the second law of thermodynamics.

2. The second law of thermodynamics is really a low-level mistake.

3. See the figure below for details.

From an excerpt from book by H B Callen, it is said that thermodynamics is time independent. Quantity energy is time independent. Can't figure out how it is time independent?

Attached image is from page number 6.

Inconel 738

temperature = 1200 °C

pressure = 10^(-8) atm

Globally, the phenomenon interpretations of the sign of: the standard Gibb′s free energy (ΔG°), the standard enthalpy (ΔH°) and the standard entropy (ΔS°) are the same in different publications.

Nevertheless, when the amount of the absolute value of one thermodynamic parameter is enough high or low, we read some small differences of interpretations, especially when there are some specific phenomenon, or adsorbent, or adsorbate, or metallic ions, etc…

The goal of this discussion is to help researchers in this field to enrich their interpretations in new experimental data by reading our different answers and replies on different situations already published.

Another delicate point which can enrich this discussion is that if one thermodynamic parameter varies slightly with temperature, how to affect the usual interpretations (the increase or decrease) for the case of positive or negative values?

What is the best free program to calculate quantum-chemical molecular descriptors, such as the total electronic energy, energies of the highest occupied and lowest unoccupied molecular orbital, and absolute electronegativity? And, for thermodynamic descriptors, like, standard Gibbs free energy and enthalpy?

Hi dear researchers

I would like to use MATLAB in order to optimization of thermodynamic cycles. I know that Refprop software can provide properties of the material. But the free version of that software dose not work appropriately. Do you have access to active version of software to share file of it with me ,please? I really need for it.

Regards

Amir

Should exergy analysis be taught to undergrad engineering students? I am wondering to what extent I should include this in my undergrad Thermodynamics course for 3rd year chemical engineering students? We do energy balance and the entropy balance already.

I am trying to implement the thermodynamic model of ejector assisted compressed air energy storage (CAES) and I need thermodynamic properties of Therminol 66 thermal oil. In the reference paper, I am following, the author utilized

**Refprop 9.1**, but I can seems to find the the Fluid "therminol 66" in the Refprop fluid library. Does it have any other name in the Refprop library?. If anyone has any idea please guide.Thank You

**Reference Article:**Hello

Kindly refer the free energy functional for systems with elements A-B and A-B-C, in the attached image.

My question is, why the gradient of the dependent element (A) appears in multi-component system (2), while not considered in binary system (1)? It would be also better if you attach any references for derivation of (2).

Thank you!

when a system say a heat engine draws heat from a hot reservoir (body at high temperature compared to the system) it does work, since heat is a low grade energy not all of heat is converted to work, therefore remaining heat is released into a cold reservoir (say to the environment, which is at lower temperature compered to the system's temperature). Now, this released heat (which is unavailable for the system) is somehow related to the entropy of the system, according to some literatures. My Question here is how is this heat related to Entropy?

The question arises from complex systems theory, in which I faced a contradiction, as earlier I thought the equilibrium state of a system means maximum order. The obstacle in my way is thermodynamics. Please help me to better understand and potentially solve this contradiction.

Hello,

I need to find experimental data for CO2 solubility in water that can be simply modeled by using the Peng Robinson equation of state for a project. The concentration of CO2 has to be very low for this purpose. I wonder if you could suggest to me a research article that contains the described experimental data for my project?

Best wishes

Water kept in a CLOSED Container at 20 degree Celsius will have a vapor pressure of 2.34 KPa, this vapor pressure is also called as saturation pressure (for pure liquids). Which means 20 degree Celsius is the saturation temperature. It is found in literatures that vapour and liquid are in equilibrium at this point. In that case we can call LIQUID water as saturated liquid and the vapours corresponding to it as saturated vapour. But when we look it from boiling phenomenon prospective, then water below 100 degree Celsius at 1 atm pressure is called as subcooled liquid. So can we call water at 20 degree celsius as subcooled liquid as well as saturated liquid??

PS I would like to request you to give me a simple explanation so that I can understand it easily.

There is a closed system containing water at 20 deg. Celsius having pressure above it 0.1 mega pascal. Now this system is heated at constant pressure. Now according to some literatures, the temperature of the water rises till 99.6 deg. celsius. At this temperature the liquid will start vaporizing and liquid at this stage is called as saturated liquid. The vapour phase is called saturated vapour. Saturated vapour and liquid co-exist in equilibrium. The temperature and pressure at which phase change occur and liquid and vapour are at equilibrium are called saturation temperature and pressure. The temperature and pr. remains constant till all the liquid gets converted to vapour.

Now I have 2 questions, i) while we heat water, and temperature rises from 20 deg. Celsius, will there be no vapor formation till 99.6 deg. Celsius?

ii) If there is phase equilibrium in the system at 99.6 deg. Celsius and 0.1 mPa, How can it be possible that all of liquid water gets converted into vapour at some point?

A high grade energy can be completely converted into a low grade energy, however visa versa is not possible for a spontaneous process. Since PE can be converted into KE but KE cannot be converted into PE when the process is spontaneous. Therefore should we consider KE is a higher grade energy like work and electrical energy?

Sodium decahydrate is Na2CO3.10H2O which is obtained by dissolving sodium carbonate in water and then crystallizing it. So can be consider it as a mixture (i.e. an impure substance) or is it a compound (pure substance)?

In what case would a reaction rate always show direct relation with activation energy or would it always be an inverse relation? Is it a indirect relation, inverse relation or both case can hold? (Please provide supporting resource, thank you).

Hello Everyone,

I am a beginner in using REFPROP software by NIST. I am trying estimate various thermodynamic properties of carbon dioxide using GERG and other equations of state. I am wondering, why I am observing a significant difference between the results of GERG-2008 and AGA8 model. Specifically the difference is in the enthalpy, entropy and internal energy.

For an example, please see the REFPROP results in the attached file. It can be seen that GERG-2008 is yielding negative and completely different values as compared to Peng-Robinson and AGA8 models. What is the reason of that variation?? How to get the similar results for comparison?

Note: I used the default reference state by REFPROP.

Regards,

Mujtaba

The reactions are as below:

CO2=CO+1/2O2

H2O=H2+1/2O2

These reactions are from syngas production.

It is meant especially thermodynamic and gas-dynamic state.

Is there any code available to calculate Spin Spin Spatial correlation function in 1d Ising model?

MgO +

**2**NaOH → Mg(OH)2 + Na2OEvolution violates the second law of thermodynamics ?. The law states that "the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium". In other words, an isolated system's entropy (a measure of the dispersal of energy in a physical system so that it is not available to do mechanical work) will tend to increase or stay the same, not decrease. Creationists argue that evolution violates this physical law by requiring an increase in order (i.e., a decrease in entropy).

Hi!

I have a protein system where a single water molecule can play a role in a ligand stabilization. To check whether this single water molecule is important in binding, I wanted to perform TI (thermodynamics integration) calculations, starting from system with water and annihilate it. My plan was to use AMBER software (PMEMD) for this purpose. I would replace water molecule with dummy atoms during TI. After many trials I finally got my tleap output (parmtop & prmcrd), but while running the script I am getting an error.

My question is: am I doing it right or there is a simpler way than TI to calculate an impact on energy after cutting our water molecule from the system?

I will be grateful for any tips!

It is becoming apparent that the configurational entropy bears no relationship with the stabilization of the so-called "high-entropy alloys" (or HEAs). I wonder if we should suppress the term "high-entropy" from these novel class of alloys and then, use the "highly-concentrated alloys" term instead.

Any ideas and/or recommendations?

How to compute physical properties (thermodynamic parameters like free energy and kinetic parameters like rate) at different pH using computational software?

Suggestions of software/open source codes that can handle the problem is highly appreciated.

Hello everyone. I hope everything is well. I read the article which is attached with this question. I have a question about thermodynamic studies. The enthalpy and entropy is calculated according to equation 4 in this paper by using linear equation in fig 10. I use 8.314 as gas constant in this equation. But I obtained different enthalpy and entropy. I do not know why this happens. Please help me find my mistakes.

It is a difficult task for me to translate my work into English, below is a try, it involves some deep topics.

**Tackling a Century Mystery: Entropy**(2008)

Introduction

Why are we still unable to explain the difficulties caused by a physical concept even after more than 150 years of hard work?

It is a very important milestone in the history of science to introduce the concept of entropy into physics, it was the first time to introduce one-way direction of change into the theory of science, and express irreversibility as the internal property of change. The introduction of the concept of entropy has had an extremely profound impact on the basic view of how science should understand existence and evolution of nature.

However, the introduction of the concept of entropy has also brought serious puzzles into physics, since the heat

*Q*is not a state variable, it is really confusing to define a state function by the aid of a path differential and an inequality. To be exact, in 1854, R.Clausius has only given a symbol without any explanation to the physical meaning of the function S, classical thermodynamics itself cannot explain clearly what entropy is, it can only talking about how the entropy will change.This is a very strange result difficult to be explain, because the concept of entropy does not seem like to involve the cognitive limits of science in our time, no one can understand what this state function is from classical literatures or any thermodynamic textbook but can only know how the state function will change, is this a perfect result?

The understanding to the entropy today we have mainly come from Boltzmann's statistical theory, in the entropy theorem, Boltzmann pointed out that entropy is proportional to the logarithm of thermodynamic probability, in H theorem, the second law was described to be the state change of thermodynamic probability, this later developed into a very popular view: entropy is a measure of disorder.

Until now, Boltzmann's statistical theory still faces a series of problems, the postulate of equal a priori probability is not applicable to the case when there are interactions within a system, such as multi-phase coexistence in thermodynamic equilibrium, liquid-liquid equilibria in a partially miscible binary system, or the segregation of alloying elements in a solid solution, and the temperature of nuclear spin system, the ordered state of Gibbs free energy, or the gravitational potential energy are some other examples. A very fact is that the postulate of equal a priori probability is not applicable to describe the ordered state of the particle distribution or the energy level distribution, this postulate is only applicable to the case when thermal motion is stronger than interactions. It is quite clear that thermodynamics does not need to consider this postulate, thus, how can one prove that Boltzmann's entropy is exactly equivalent to thermodynamic entropy?

What is puzzling is that we already know that we cannot discuss the second law when ignored the dissipation factors such as friction and viscosity, we also know that these dissipation factors are obviously related to the interactions but not the result of the postulate of equal a priori probability. Whereas, in statistical theory, near independent subsystems or statistical ensemble are the main models to discuss the entropy and the second law, in such ideological system, how can we discuss the dissipation factors such as friction and viscosity?

*H*theorem have been stumped by the ‘’inversion paradox’’ proposed by J.Loshimidt in 1876, it is also unable to explain the ‘’circular paradox’’ proposed by E.Zermelo based on Poincare recurrence theorem. Boltzmann himself later realized that the H-quantity model as a solution to explain the irreversibility derived from dynamics still has problems that are difficult to explain, it is only a phenomenological model, just as K.R.Poper said: ‘’Boltzmann failed to clarify the state of H theorem, nor did he explain clearly the increase in entropy’’.[1]

Another problem is: since there has been no monotonous function similar to thermodynamic entropy in dynamics, the general mathematical properties of the fundamental laws of dynamics (inversion symmetry) indicate that the dynamic "changes" are reversible. The explanation of the state of thermodynamic probability further revealed the contradictory that the description about the direction of changes and time in thermodynamics and dynamics are different. Since the explanation of thermodynamic probability cannot be applied to describe the direction of microscopic state change, this means that there will be no irreversibility in dynamics in the sense of the second law. This leads to the conflict between the two theoretical systems on the view of nature, in physics, we have been unable to establish the relations on the concepts of the direction of changes and time between dynamics and thermodynamics, the former describes to us a world without evolution, and the latter expresses the evolution as the unfolding of the second law.

Physicists usually regard Boltzmann's statistical theory as a scheme to establish the connection from the dynamics of the basic process to the thermodynamics of the statistical system, but this scheme has not been able to give complete results, and its scope of application has always been ambiguous. The description given by statistical probability shows the view that there is no microscopic explanation of entropy and irreversibility at the basic dynamics level. In this sense, Boltzmann approach leads to a complete separation between basic dynamic process and statistical collective behavior in the description on the direction of change and time, this doesn't seem like a real image of the world around us, for example, we can feel the existence of one-way direction of change from the beep of a radioactive decay counter, but this is not the unidirectionality expressed by Boltzmann's statistical theory, we also can hardly understand how to deduce the irreversible and non-deterministic theory from the reversible and deterministic dynamics.

From the 1850s to the present, in the following 150 years, the contradictory issues concerning the physical meaning of entropy and the different descriptions in the direction of change and time between dynamics and thermodynamics have become one of the core problems in the views of existence and evolution. Since the unidirectionality revealed by the second law of thermodynamics involves the direction of change and the meaning of time, this issue is related to our basic views on existence and evolution of nature. Many scientists believe that the second law is an approximate result, however, though a series of appeasement explanations have been given, the initial problems have never changed in more than 150 years, we still have to repeat the problem again and again that has aroused strong feelings over the past 150 years:

What is entropy?

What are the irreversible changes taking place?

[1] Not the original text.

*Since that second law of thermodynamics has a very special role in all branches of science, this law has been established with different approaches and formulations. Although Carnot introduced the irreversible process as well as irreversibility concept, Clausius formulated the second law of classical thermodynamics inspired by them as well as introducing entropy quantity for thermodynamical cycles. Clausius formulation defines thermodynamical entropy as a time direction for all physical processes. In fact, entropy and its significance are becoming an important challenge between scientists. Also, general branches of physics define entropy with general approaches that using them, the second law of classical thermodynamics can be extracted. In all these general approaches, energy and, generally energy levels have the main role for extracting the second law of thermodynamics.*

*Is the supposition of the unified field theory compatible with the Second Law of Thermodynamics?*

I performed constrained MD in CP2K, and I obtained the average force along the reaction coordinate by averaging

**Lagrange multipliers**using the script provided. Now, I require a free energy profile. It is evident that thermodynamic integration needs to be performed. I was wondering if there is any script or software to plot the same?Carnot efficiency can be calculated by the first and second laws of thermodynamics. Which one would you like to choose?

See the following article for details