
Bjarne AndresenUniversity of Copenhagen · Niels Bohr Institute
Bjarne Andresen
Dr. scient.
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Publications (155)
The cornerstone of finite-time thermodynamics is all about the price of haste and how to minimize it. Reversible processes may be ultimately efficient, but they are unrealistically slow. In all situations-chemical, mechanical, economical-we pay extra to get the job done quickly. Finite-time thermodynamics can be used to develop methods to limit tha...
This paper extends the concept of epitropy, as introduced in previous work, to capture the effects of extreme tail behavior arising naturally over very long time and large space scales. Epitropy has some qualities that parallel entropy, although it is not quite the same. Its function is to capture the effects of a probability distribution function...
Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs–Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosi...
In this work, we lay the foundations for computing the behavior of a quantum heat engine whose working medium consists of an ensemble of non-harmonic quantum oscillators. In order to enable this analysis, we develop a method based on the Schrödinger picture. We investigate different possible choices on the basis of expanding the density operator, a...
Typical human-scaled considerations of thermodynamic states depend primarily on the core of associated speed or other relevant distributions, because the wings of those distributions are so improbable that they cannot contribute significantly to averages. However, for long timescale regimes (slow time), previous papers have shown otherwise. Fluctua...
The dissipation in an irreversible step process is reduced when the number of steps is increased in any refinement of the steps in the process. This is a consequence of the ladder theorem, which states that, for any irreversible process proceeding by a sequence of relaxations, dividing any relaxation step into two will result in a new sequence that...
Context
The way organisms are patterned in space dictates the outcome of many ecological processes such as growth, survival, colonization, and migration. The field of landscape ecology has developed quantitative metrics to describe spatial patterning using the concept of entropy. However, a general theory of how these patterns relate to one another...
From the viewpoint of thermodynamics at a finite time, the limiting possibilities of mechanical separation systems are considered. Lower limits of energy expenditure are obtained for separation systems with a given performance. It is shown that these expenditures do not tend to zero, when one of the components of the mixture being separated tends t...
Finite-time thermodynamics was created 45 years ago as a slight modification of classical thermodynamics, by adding the constraint that the process in question goes to completion within a finite length of time [...]
We analyze limiting capabilities of mechanical separation processes using finite-time thermodynamics and obtain estimates for the lower bound of the energy consumption for systems of a given productivity. We show that this consumption does not tend to zero when the molar fraction of one of the components tends to unity. The estimates obtained are u...
The conditions for minimum dissipation and the dependence of the minimum possible entropy production on the heat load are obtained for heat exchange systems with a given heat load and total heat transfer coefficient. The case of variable heat capacity of streams is considered. Distributions of heat exchange coefficients and heat capacity rates of t...
Coherent control of self-contained quantum systems offers the possibility to fabricate smallest thermal transistors. The steady coherence created by the delocalization of electronic excited states arouses nonlinear heat transports in non-equilibrium environment. Applying this result to a three-level quantum system, we show that quantum coherence gi...
We continue our exploration of thermodynamics at long observational timescales, “slow time,” by including turbulent dynamics leading to a condition of fluctuating local equilibrium. Averaging these fluctuations in wind speed and temperature results in a velocity distribution with heavy tails which, however, are necessarily truncated at some large m...
Any observation, and hence concept, is limited by the time and length scale of the observer and his instruments. Originally, we lived on a timescale of minutes and a length scale of meters, give or take an order of magnitude or two. Therefore, we devloped laboratory sized concepts, like volume, pressure, and temperature of continuous media. The pas...
The first paper published as Finite-Time Thermodynamics is from 1977 [...]
This work proposes a structure synthesis and surface distribution algorithm in a heat exchange system for the case when all heat capacity rates and inlet temperatures of the hot streams are constant, while cold streams also have outlet temperatures set. The algorithm includes the possibility of changing the phase state of the contacting streams. Th...
We consider the problem of optimal parametric control for a single oscillator or an ensemble of oscillators due to a change in one of the coefficients of the system of equations characterizing them. We obtain solutions for the problem of finding the maximal change in the energy of oscillations for a given time.
Coherent control of self-contained quantum systems offers the possibility to fabricate smallest thermal transistors. The steady coherence created by the delocalization of electronic excited states arouses nonlinear heat transports in non-equilibrium environment. Applying this result to a three-level quantum system, we show that quantum coherence gi...
An overall synthesis of biology and non-equilibrium thermodynamics remains a challenge at the interface between the physical and life sciences. Herein, theorems from finite-time and control thermodynamics are applied to biological processes to indicate which biological strategies will succeed over different time scales. In general, living systems m...
We show that the inability of a quantum Otto cycle to reach a limit cycle is connected with the propagator of the cycle being non-compact. For a working fluid consisting of quantum harmonic oscillators, the transition point in parameter space where this instability occurs is associated with a non-hermitian degeneracy (exceptional point) of the eige...
We show that the inability of a quantum Otto cycle to reach a limit cycle is connected with the propagator of the cycle being non-compact. For a working fluid consisting of quantum harmonic oscillators, the transition point in parameter space where this instability occurs is associated with a non-hermitian degeneracy (exceptional point) of the eige...
If one could exist on climate scales would it make any more sense to measure laboratory-scale quantities to capture climate conditions than it does for us on the laboratory scale to compute wave functions to understand the weather? Clearly the quantum mechanical and the laboratory regime are constructed in terms of different physical variables. Why...
We investigate the importance of the time and length scales at play in our descriptions of Nature. What can we observe at the atomic scale, at the laboratory (human) scale, and at the galactic scale? Which variables make sense? For every scale we wish to understand we need a set of variables which are linked through closed equations, i.e., everythi...
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final...
The total cost of ownership is calculated for a combined heating and humidification coil of an air-handling unit taking into account investment and operation costs simultaneously. This total cost represents the optimization function for which the minimum is sought. The parameters for the cost dependencies are the physical dimensions of the coil: le...
The traditional connection between rate constants and free energy landscapes is extended to define effective free energy landscapes relevant on any chosen timescale. Although the Eyring-Polanyi transition state theory specifies a fixed timescale of tau = h/k(B)T, we introduce instead the timescale of interest for the system in question, e.g. the ob...
We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold's, has achieved widespread use. Lengths calculated based on this metric have been used to bound dissipation in finite-time (irreversible) processes be they continuous or discrete, and described in the energy picture or the entropy picture. Examples...
We extend Maxwellian velocity distributions to long observational timescales in much the same way that short timescale statistical mechanics distributions are averaged to yield normal laboratory timescale thermodynamic distributions. This long timescale view has several novel effects: Fluctuating overall velocities (i.e. “wind”) thermalizes into an...
Standard thermodynamics allows spontaneous reactions if their change of free energy ?G = 0. Following the tradition of thermodynamics, the author proposes to put the finite-time impossibility principle into the form of the nonexistence of Perpetual Motion Machines of the Third Kind (PM3). PM3 formalizes the statement that site-specific recombinatio...
The field of finite-time thermodynamics considers questions such as: does dissipation necessarily occur if a thermodynamic process takes place in finite time. This chapter presents four concepts: the tricycle, thermodynamic length, work deficiency, and network thermodynamics. These concepts highlight the basic features of finite-time thermodynamics...
Functions, not dynamical equations, are the definitive mathematical objects in equilibrium thermodynamics. However, more than one function is often described as "the" equation of state for any one physical system. Usually these so named equations only capture incomplete physical content in the relationships between thermodynamic variables, while ot...
The problem of effectively adiabatic control of a collection of classical harmonic oscillators sharing the same time-dependent frequency is analyzed. The phase differences between the oscillators remain fixed during the process. This fact leads us to adopt the coordinates: energy, Lagrangian, and correlation, which have proved useful in a quantum d...
Cystic fibrosis (CF) is a chronic progressive pulmonary disorder caused by mutations in the CFTR (cystic fibrosis transmembrane conductance regulator) gene. A CF lung is generally characterized by obstructed airflow to an extent that leads to destruction of airway wall support structure. Airway resistance, resulting from both laminar and turbulent...
In this paper an invariant of motion for Hamiltonian systems is introduced: the Casimir companion. For systems with simple dynamical algebras (e.g., coupled spins, harmonic oscillators) our invariant is useful in problems that consider adiabatically varying the parameters in the Hamiltonian. In particular, it has proved useful in optimal control of...
The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with...
We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy E T from a given initial state (q i , p i) by controlling its frequency ω, ω min ω ω max . A brief synopsis of optimal control theory is included and the solution for the harmonic oscillator problem is used to illustrate the theory...
Das Leitmotiv der Thermodynamik in endlicher Zeit (“finite-time thermodynamics”) ist der Preis der Ungeduld und seine Minimierung. Reversible Prozesse können vollständig effizient sein, laufen jedoch meist unverhältnismäßig langsam ab. In allen Situationen – chemisch, mechanisch oder ökonomisch – sind wir bereit, mehr zu zahlen, damit eine Aufgabe...
In the part I of this paper we investigated how the energy carried by warm water can be best used for heating the outdoor cold air while increasing its humidity in cold seasons. We set to check the optimal width of a humidifier/heater that will offer the transfer of mass and energy between air and water with the minimum of entropy production. The m...
The fundamental heat transfer and humidity control processes are considered and the polytropic process of heating air while modifying the humidity contents is analyzed using the optimal control theory. The aim is to investigate optimal ways of heating and humidifying the air while producing minimum entropy. Heating and humidification are considered...
A finite-time generic model to describe the behavior of real refrigeration systems is discussed. The model accounts for finite heat transfer rates, heat leaks, and friction as different sources of dissipation. The performance characteristics are cast in terms of cooling rate () versus coefficient of performance
(). For comparison purposes, various...
The set of solutions inferred by the generic maximum entropy (MaxEnt) or
maximum relative entropy (MaxREnt) principles of Jaynes - considered as a
function of the moment constraints or their conjugate Lagrangian multipliers -
is endowed with a Riemannian geometric description, based on the second
differential tensor of the entropy or its Legendre t...
Carefully specifying the entropy flow and entropy generation in a system is essential when optimizing its performance. Here we mention that in an ensemble some copies may seemingly violate the second law of thermodynamics, which is OK if on average entropy is produced. We focus on which quantity is being optimized and the need for controls to achie...
Nej, det er fundamentalt termodynamisk umuligt at definere en gennemsnitstemperatur af noget som helst. Denne kategoriske, og termodynamisk set ganske elementære, udtalelse har vakt en hel del furore, siden vi publicerede den for godt et år siden, for når der ikke findes en global gennemsnitstemperatur, hvordan kan den så være steget i nyere tid, o...
Physical, mathematical, and observational grounds are employed to show
that there is no physically meaningful global temperature for the Earth
in the context of the issue of global warming. While it is always
possible to construct statistics for any given set of local temperature
data, an infinite range of such statistics is mathematically permissi...
Beam-foil excitation functions have been measured for some optical transitions in C II-C IV in the projectile energy range 100-450 keV, and in C IV-C VI from 4 to 20 MeV. The full set of population functions, representing eight different classes of core-outer shell arrangements, are reproduced by three parameters accounting for 1s vacancies, 2s vac...
Optimal piston motion is derived for adiabatic processes in the presence of different types of friction and with frictional energy dissipated externally as well as internally. The assumed model for the frictional dissipation affects the optimal motion. We consider a piston fitted in a cylinder containing an ideal gas as the working fluid. The gas s...
A generic model of an endoreversible engine is developed for studying the effect of convective heat transfer, the rate of which depends on the temperature difference to the power n where n is close to unity. The efficiency at maximum power production is found to have as its principal part the
Curzon-Ahlborn [Am. J. Phys. 43, 22 (1975)]
expression...
General principles of inversion in connection with thermodynamic length optimizations on discrete systems are used to specify the optimal temperature of each tray in a distillation column and consequently the amount of heat to be added or withdrawn in order to maintain that temperature. The thermal efficiency of the distillation column may be impro...
Oxygen delivery to the tissues is crucial to survival but our understanding of the pro-cesses involved in the transport of oxygen from blood to tissue is incomplete. The aim of the present work is to illustrate a long-standing paradox regarding such trans-port by reporting new state-of-the-art measurements and by analyzing the results in several wa...
While endoreversible heat-to-power conversion systems operating be- tween two heat reservoirs have been intensely studied, systems with several reservoirs have attracted little attention. Here we analyse the maximum power processes of such systems with stationary temperature reservoirs. We find that independent of the number of reservoirs the worki...
Diabatic distillation is a separation process in which heat is transferred on the trays inside the column as opposed to classical adiabatic columns where heat is only supplied to the reboiler and extracted from the condenser. Such diabatic columns dramatically reduce the exergy needed to perform the separation. One implementation, particularly suit...
The maximum power processes of multi-source endoreversible engines with stationary temperature reservoirs are investigated. We prove that the optimal solution is always time independent with a single hot and a cold engine contact temperature. The heat reservoirs fall into three groups: the hot reservoirs which are connected at all times for heat de...
Viruses are the most common biological entities in the oceans by an order of magnitude. However, very little is known about their diversity. Here we report a genomic analysis of two uncultured marine viral communities. Over 65% of the sequences were not significantly similar to previously reported sequences, suggesting that much of the diversity is...
We analyze the maximum obtainable yield of B, starting from A in the consecutive chemical reactions ABC. We use the temperature as the control variable for a given process duration. We show that all optimal paths start with a branch at infinite temperature and derive a curve on which switching from this temperature to lower temperatures is possible...
General optimization results from physics indicate that maximum efficiency of a process, in the sense of minimum overall entropy production, is achieved when the rate of entropy production is constant over time, however not in ordinary clock time but on an, in general varying, "eigen time" scale, intrinsic to the system. We identify the eigen time...
A distillation column with the possibility of heat exchange on every tray (a fully diabatic column) is optimized in the sense of minimizing its total entropy production. This entropy production counts the interior losses due to heat and mass flow as well as the entropy generated in the heat exchangers. It is observed that the optimal heating distri...
In his paper D. P. Sekulic [J. Appl. Phys. 83, 4561 (1998)] advances a number of arguments about finite-time thermodynamics which call for refutation as well as comment. It provides an opportunity to put into print a clarification of just what finite-time thermodynamics is, what it is not, and how it is related to some of the other, parallel effort...
Recently, the concept of equal thermodynamic distance (ETD) has been proposed to minimize entropy production in a distillation process using a diabatic column. ETD gives the optimal temperature profile to first-order in N−1, where N is the number of trays. ETD, however, does not generally give the true minimum for distillation columns with few tray...
We show that Nernst's original postulate follows directly from a
vanishing heat capacity at zero temperature without further
constraints. Thermodynamic stability of the system along with the
independence of the other thermodynamic state variables ensures a
sufficiently slow temperature approach to zero that the change of
the entropy of the system v...
Two theoretically derived entropy optimization methods for design of distillation columns with multiple heat exchangers have recently been presented in the literature. These two methods, called equal thermodynamic distance (ETD) and equipartition of forces (EoF), have here been applied to binary distillation and compared. For a 17 plate column sepa...
It is acknowledged that the Curzon–Ahlborn efficiency ηCA determines the efficiency at maximum power production of heat engines only affected by the irreversibility of finite rate heat transfer (endoreversible engines), but ηCA is not the upper bound of the efficiencies of heat engines. This is conceptually different from the role of the Carnot eff...
the date of receipt and acceptance should be inserted later Abstract. Optimization of processes can yield a variety of answers, depending not only on the objective of the optimization but also on the constraints that define the problem. Within the context of thermodynamic optimization, the role of the constraints is particularly important because,...
In this paper investigations regarding optimal placement and duty distribution of internal heat exchangers in distillation columns have been carried out based on simulations. In particular the effect of adding 2, 4 and 19 internal heat exchangers to a 19 tray distillation column separating 2-propanol and methanol was studied. It is concluded that t...
The thermal efficiency of a distillation column may be improved by permitting heat exchange on every tray rather than only in the reboiler and the condenser. Thermodynamic length optimizations on discrete systems specify the optimal temperature of each tray and consequently the amount of heat to be added or withdrawn in order to maintain that tempe...
The thermal efficiency of a distillation column may be improved by permitting heat exchange on every tray rather than only in the reboiler and the condenser. Thermodynamic length optimizations on discrete systems specify the optimal temperature of each tray and, consequently, the amount of heat to be added or withdrawn in order to maintain that tem...
The cyclic models established by Goktun and Yavuz are used to analyze the influence of thermal resistances in the heat exchange processes and internal irreversibilities in the working fluid on the performance of combined heat pump cycles. A number of significant results are derived. The results obtained here show clearly that there are some obvious...
The thermal efficiency of a distillation column may be improved by permitting heat exchange on every tray rather than only in the reboiler and the condenser. Thermodynamic length optimizations on discrete systems specify the optimal temperature of each tray and consequently the amount of heat to be added or withdrawn in order to maintain that tempe...
The Monte Carlo optimisation technique simulated annealing has been used to sample the possible values of the permanent of fully indecomposable (0,1)-matrices. The basic idea in simulated annealing is that a Markov chain explores the space of feasible solutions, each of which has an associated “energy” (here minus the permanent of the matrix).The c...
It is shown that for three different arrangements of heat resistances the standard optimum performance criteria of endoreversible Carnot engines at maximum power output can be conveniently expressed by two simple diagrams. It is also pointed out that such diagrams should rightfully be referred to as Bejan diagrams.
Finite-time thermodynamics was ‘invented’ in 1975 by R. S. Berry, P. Salamon, and myself as a consequence of the first world oil crisis. It simply dawned on us that all the existing criteria of merit were based on reversible processes and therefore were totally unrealistic for most real processes. That made an evaluation of the potential for improv...
Using computer experiments on a simple three-state system and an NP-complete system of permanents we compare different proposed simulated annealing schedules in order to find the cooling strategy which has the least total entropy production during the annealing process for given initial and final states and fixed number of iterations. The schedules...
A solar-driven Stirling engine is modelled as a combined system which consists of a solar collector and a Stirling engine. The performance of the system is investigated, based on the linearized heat loss model of the solar collector and the irreverisible cycle model of the Stirling engine affected by finite-rate heat transfer and regenerative losse...
A single endoreversible engine can operate as a cooler, a true heat engine, a heat pump, or a refrigerator. We investigate how many different modes of operation a combined system of two endoreversible engines may display. Special attention is paid to the independent combined system which neither consumes nor supplies power.
The influence of three main irreversibilities existing in thermoelectric devices on the performance of a thermoelectric generator is investigated by means of nonequilibrium thermodynamics and finite-time thermodynamics. The efficiency and the power output of the thermoelectric generator are optimized. The maximum efficiency and the maximum power ou...
Finite-time thermodynamics is the extension of traditional thermodyamics to deal with processes which have explicit time or rate dependencies. In doing so the macroscopic measurable description of thermodynamic systems is preserved while irreversibilities, and the hence entropy production, are introduced via empirical rate equations or imposed cons...
We investigate whether it is possible to operate a given binary distillation column with several different reflux ratios (heat flow rates) while achieving the same purity and amount of distillate. We find that even for small variations in the plate efficiency vs flow rate several distinct values of the reflux ratio exist that achieve the same outpu...
We investigate the optimization of chemical reactions of the type nA mB in a closed container. The goal is to produce a maximal amount of A or B within a given finite time. The controls are taken to be volume and temperature, restricted to allowed regions in (V,β)-space with β = 1/kT. We show that the optimal path is achieved by choosing V and β su...
The effect of three main irreversibilities existing in thermoelectric devices on the performance of a thermoelectric heat pump is investigated. The coefficient of performance and the heating load of the heat pump are derived. The optimal performance of the heat pump at maximum coefficient of performance is discussed, and the rational working region...
The methods of finite-time thermodynamics are complemented with some probabilistic concepts allowing a more accurate description of the performance indicators of a power system. A chemical reaction is studied. The model is a flow reactor coupled by a heat exchanger to an engine. The probabilistic approach put into evidence the existence of a maximu...
The cycle model of a heat-engine-driven heat pump is used to study the performance of an absorption heat pump affected by heat resistances. The coefficient of performance of the absorption heat pump is adopted to be the objective function for optimization. The optimal regions of the coefficient of performance and the specific heating load are deter...
For an arbitrary finite-time thermodynamic or information-based process we derive a lower bound on cumulative entropy production, as well as the associated optimal operating strategy for minimizing entropy production. The optimal path corresponds to a fixed rate of entropy production in the system, provided the rate of change is calculated in terms...
Several key problems previously analyzed by simulated annealing are well described by a simple two-state statistical mechanical model, equivalent to the one-dimensional Ising model, in conjunction with an Arrhenius type rate equation. With this model we develop an analytic solution for the optimal cooling strategy which computationally is much fast...
For a common class of finite-time heat transfer processes, we derive optimal heating and cooling strategies for minimizing entropy generation. Solutions pertain to a generalized heat transfer law, and are illustrated quantitatively for cases of practical interest, including Newtonian and radiative heat transfer. Optimal paths are compared with the...
The optimal heating or cooling strategy that minimizes entropy production is derived for a simple class of common heat transfer processes that are constrained to proceed in a fixed, finite time. The empirical wisdom embodied in conventional single‐pass counterflow heat exchanger design is examined in light of this solution. For judiciously selected...
Simulated annealing is a global optimization procedure (Kirkpatrick et al. 1983) which exploits an analogy between combinatorial optimization problems and the statistical mechanics of physical systems. The analogy gives rise to an algorithm for finding near-optimal solutions to the given problem by simulating the cooling of the corresponding physic...
A new generalization of the Plateau problem that includes the constraint of enclosing a given region is introduced. Physically, the problem is important insofar as it bears on sintering processes and the structure of wetted porous media. Some primal and dual characterizations of the solutions are offered and aspects of the problem are illustrated i...
The availability loss -DeltaAu in a process is equal to the flow of the extensive thermodynamic quantities multiplied by the respective intensity differences only if the degraded work, the ``uncompensated heat'' of Clausius, is disposed of into the environment. We define work deficiency as the above product in all situations and relate it to the di...
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