Special Issue "Finite-Time Thermodynamics"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (31 August 2020).

Special Issue Editors

Prof. R. Stephen Berry
E-Mail Website
Guest Editor
Department of Chemistry, The University of Chicago, 5735 S. Ellis Ave, Chicago, IL 60637, USA
Interests: finite-time thermodynamics; structures, properties, and dynamics of clusters and biopolymers; dynamics of few-body systems
Prof. Dr. Peter Salamon
E-Mail Website
Guest Editor
Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-7720, USA
Interests: finite-time thermodynamics; geometrical thermodynamics; biomathematics; optimization and mathematical modeling
Prof. Bjarne Andresen
E-Mail Website
Guest Editor
Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
Interests: finite-time thermodynamics(FTT); application of FTT ideas in a wide range of areas; quantum, chemical, and biological systems; global optimization theory; thermodynamic geometry; thermodynamics at extreme time and length scales

Special Issue Information

Dear Colleagues,

Even though finite-time thermodynamics (FTT) is already 45 years old by now, it is still in its adolescent stage. The original horizon of classical thermodynamics with the one feature of a specified process completion time added has long been broken. Topics treated have expanded into quantum systems, engineering design, biology and evolution, information theory, and economics, just to name a few, and the way of thinking, in particular using the concept of thermodynamic geometry, has inspired, e.g., general optimization theory. FTT continues to expand into new areas where either we are interested in calculating “the cost of haste”, or we want to optimize the path of a process within given constraints. FTT has just started.

In this Special Issue on FTT, we want to show the full breadth and depth of the field, and thus, we will interpret finite-time thermodynamics broadly, both in terms of the methods used to investigate all the effects of a finite time horizon for the processes in question, and in terms of the objects investigated. In other words, the objects must not necessarily be of a thermodynamic nature but could also be engineering, economics, optimization, scheduling, and anywhere else thermodynamic thinking is useful. We also want to look ahead just as much as look back. Therefore, we welcome novel, yet untested, ideas and visions just as much as finalized research results. We hope to receive many inspiring contributions.

Prof. R. Stephen Berry
Prof. Peter Salamon
Prof. Bjarne Andresen
Guest Editors

Manuscript Submission Information

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Keywords

  • Finite-time thermodynamics
  • Thermodynamic geometry
  • Control thermodynamics
  • Biological optimization
  • Control economics
  • Optimal control modelling

Published Papers (19 papers)

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Article
Optimization, Stability, and Entropy in Endoreversible Heat Engines
Entropy 2020, 22(11), 1323; https://doi.org/10.3390/e22111323 - 20 Nov 2020
Cited by 6 | Viewed by 720
Abstract
The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that [...] Read more.
The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that the system has a stationary fixed point, along with a Taylor expansion in the first order of the input/output heat fluxes, without further specifications regarding the properties of the working fluid or the heat device specifications. Specific cases of the Newton and the phenomenological heat transfer laws in a Carnot-like heat engine model were analyzed. It was shown that the evolution of the trajectories toward the stationary state have relevant consequences on the performance of the system. A major role was played by the symmetries/asymmetries of the conductance ratio σhc of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small σhc values, the thermodynamic trajectories evolved near the endoreversible limit, improving the efficiency and power output values with a decrease in entropy generation; (2) for large σhc values, the thermodynamic trajectories evolved either near the Pareto front or near the endoreversible limit, and in both cases, they improved the efficiency and power values with a decrease in entropy generation; (3) for the symmetric case (σhc=1), the trajectories evolved either with increasing entropy generation tending toward the Pareto front or with a decrease in entropy generation tending toward the endoreversible limit. Moreover, it was shown that the total entropy generation can define a time scale for both the operation cycle time and the relaxation characteristic time. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine
Entropy 2020, 22(11), 1255; https://doi.org/10.3390/e22111255 - 04 Nov 2020
Cited by 13 | Viewed by 733
Abstract
Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin [...] Read more.
Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Thermodynamic Curvature of the Binary van der Waals Fluid
Entropy 2020, 22(11), 1208; https://doi.org/10.3390/e22111208 - 26 Oct 2020
Cited by 1 | Viewed by 837
Abstract
The thermodynamic Ricci curvature scalar R has been applied in a number of contexts, mostly for systems characterized by 2D thermodynamic geometries. Calculations of R in thermodynamic geometries of dimension three or greater have been very few, especially in the fluid regime. In [...] Read more.
The thermodynamic Ricci curvature scalar R has been applied in a number of contexts, mostly for systems characterized by 2D thermodynamic geometries. Calculations of R in thermodynamic geometries of dimension three or greater have been very few, especially in the fluid regime. In this paper, we calculate R for two examples involving binary fluid mixtures: a binary mixture of a van der Waals (vdW) fluid with only repulsive interactions, and a binary vdW mixture with attractive interactions added. In both of these examples, we evaluate R for full 3D thermodynamic geometries. Our finding is that basic physical patterns found for R in the pure fluid are reproduced to a large extent for the binary fluid. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Perturbed and Unperturbed: Analyzing the Conservatively Perturbed Equilibrium (Linear Case)
Entropy 2020, 22(10), 1160; https://doi.org/10.3390/e22101160 - 15 Oct 2020
Viewed by 642
Abstract
The “conservatively perturbed equilibrium” (CPE) technique for a complex chemical system is computationally analyzed in a batch reactor considering different linear mechanisms with three and four species. Contrary to traditional chemical relaxation procedures, in CPE experiments only some initial concentrations are modified; other [...] Read more.
The “conservatively perturbed equilibrium” (CPE) technique for a complex chemical system is computationally analyzed in a batch reactor considering different linear mechanisms with three and four species. Contrary to traditional chemical relaxation procedures, in CPE experiments only some initial concentrations are modified; other conditions, including the total amount of chemical elements and temperature are kept unchanged. Generally, for “unperturbed” species with initial concentrations equal to their corresponding equilibrium concentrations, unavoidable extreme values are observed during relaxation to the equilibrium. If the unperturbed species is involved in one step only, this extremum is a momentary equilibrium of the step; if the unperturbed species is involved in more reactions, the extremum is not a momentary equilibrium. The acyclic mechanism with four species may exhibit two extrema and an inflection point, which corresponds to an extremum of the rate of the species change. These facts provide essential information about the detailed mechanism of the complex reaction. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Radiative Transfer and Generalized Wind
Entropy 2020, 22(10), 1153; https://doi.org/10.3390/e22101153 - 14 Oct 2020
Cited by 2 | Viewed by 436
Abstract
Dissimilar flows can be compared by exploiting the fact that all flux densities divided by their conjugate volume densities form velocity fields, which have been described as generalized winds. These winds are an extension of the classical notion of wind in fluids which [...] Read more.
Dissimilar flows can be compared by exploiting the fact that all flux densities divided by their conjugate volume densities form velocity fields, which have been described as generalized winds. These winds are an extension of the classical notion of wind in fluids which puts these distinct processes on a common footing, leading to thermodynamical implications. This paper extends this notion from fluids to radiative transfer in the context of a classical two-stream atmosphere, leading to such velocities for radiative energy and entropy. These are shown in this paper to exhibit properties for radiation previously only thought of in terms of fluids, such as the matching of velocity fields where entropy production stops. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Thermoelectric Efficiency of Silicon–Germanium Alloys in Finite-Time Thermodynamics
Entropy 2020, 22(10), 1116; https://doi.org/10.3390/e22101116 - 02 Oct 2020
Cited by 3 | Viewed by 465
Abstract
We analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon–Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The [...] Read more.
We analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon–Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The thermoelectric efficiency of that system as function of the composition and of the effective temperature gradient is calculated as well. For three different temperatures (T=300 K, T=400 K, T=500 K), we determine the values of composition and thermal conductivity corresponding to the optimal thermoelectric energy conversion. The relationship of our approach with Finite-Time Thermodynamics is pointed out. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Thermodynamics at Very Long Time and Space Scales
Entropy 2020, 22(10), 1090; https://doi.org/10.3390/e22101090 - 28 Sep 2020
Cited by 6 | Viewed by 497
Abstract
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, [...] Read more.
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 past 150 years we managed to observe on the molecular scale and similarly nanoseconds timescale, leading to atomic physics that requires new concepts. In this paper, we are moving in the opposite direction, to extremely large time and length scales. We call this regime “slow time”. Here, we explore which laboratory concepts still apply in slow time and which new ones may emerge. E.g., we find that temperature no longer exists and that a new component of entropy emerges from long time averaging of other quantities. Just as finite-time thermodynamics developed from the small additional constraint of a finite process duration, here we add a small new condition, the very long timescale that results in a loss of temporal resolution, and again look for new structure. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Geometric Optimisation of Quantum Thermodynamic Processes
Entropy 2020, 22(10), 1076; https://doi.org/10.3390/e22101076 - 24 Sep 2020
Cited by 9 | Viewed by 1128
Abstract
Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We review and connect different frameworks where it emerges in the quantum regime: [...] Read more.
Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We review and connect different frameworks where it emerges in the quantum regime: adiabatically driven closed systems, time-dependent Lindblad master equations, and discrete processes. A geometric lower bound on entropy production in finite-time is then presented, which represents a quantum generalisation of the original classical bound. Following this, we review and develop some general principles for the optimisation of thermodynamic processes in the linear-response regime. These include constant speed of control variation according to the thermodynamic metric, absence of quantum coherence, and optimality of small cycles around the point of maximal ratio between heat capacity and relaxation time for Carnot engines. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Optimal Control of Hydrogen Atom-Like Systems as Thermodynamic Engines in Finite Time
Entropy 2020, 22(10), 1066; https://doi.org/10.3390/e22101066 - 23 Sep 2020
Cited by 4 | Viewed by 590
Abstract
Nano-size machines are moving from only being topics of basic research to becoming elements in the toolbox of engineers, and thus the issue of optimally controlling their work cycles becomes important. Here, we investigate hydrogen atom-like systems as working fluids in thermodynamic engines [...] Read more.
Nano-size machines are moving from only being topics of basic research to becoming elements in the toolbox of engineers, and thus the issue of optimally controlling their work cycles becomes important. Here, we investigate hydrogen atom-like systems as working fluids in thermodynamic engines and their optimal control in minimizing entropy or excess heat production in finite-time processes. The electronic properties of the hydrogen atom-like system are controlled by a parameter κ reflecting changes in, e.g., the effective dielectric constant of the medium where the system is embedded. Several thermodynamic cycles consisting of combinations of iso-κ, isothermal, and adiabatic branches are studied, and a possible a-thermal cycle is discussed. Solving the optimal control problem, we show that the minimal thermodynamic length criterion of optimality for finite-time processes also applies to these cycles for general statistical mechanical systems that can be controlled by a parameter κ, and we derive an appropriate metric in probability distribution space. We show how the general formulas we have obtained for the thermodynamic length are simplified for the case of the hydrogen atom-like system, and compute the optimal distribution of process times for a two-state approximation of the hydrogen atom-like system. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Minimum Entropy Generation Rate and Maximum Yield Optimization of Sulfuric Acid Decomposition Process Using NSGA-II
Entropy 2020, 22(10), 1065; https://doi.org/10.3390/e22101065 - 23 Sep 2020
Cited by 7 | Viewed by 580
Abstract
Based on the theory of finite-time thermodynamics (FTT), the effects of three design parameters, that is, inlet temperature, inlet pressure, and inlet total mole flow rate, of a tubular plug-flow sulfuric acid decomposition reactor on the total entropy generation rate (EGR) and SO [...] Read more.
Based on the theory of finite-time thermodynamics (FTT), the effects of three design parameters, that is, inlet temperature, inlet pressure, and inlet total mole flow rate, of a tubular plug-flow sulfuric acid decomposition reactor on the total entropy generation rate (EGR) and SO2 yield are analyzed firstly. One can find that when the three design parameters are taken as optimization variables, the minimum total EGR and the maximum SO2 yield of the reference reactor restrict each other, i.e., the two different performance objectives cannot achieve the corresponding extremum values at the same time. Then, the second-generation non-dominated solution sequencing genetic algorithm (NSGA-II) is further used to pursue the minimum total EGR and the maximum SO2 yield of the reference reactor by taking the three parameters as optimization design variables. After the multi-objective optimization, the reference reactor can be Pareto improved, and the total EGR can be reduced by 9% and the SO2 yield can be increased by 14% compared to those of the reference reactor. The obtained results could provide certain theoretical guidance for the optimal design of actual sulfuric acid decomposition reactors. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
The Quantum Friction and Optimal Finite-Time Performance of the Quantum Otto Cycle
Entropy 2020, 22(9), 1060; https://doi.org/10.3390/e22091060 - 22 Sep 2020
Cited by 6 | Viewed by 694
Abstract
In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider [...] Read more.
In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Modeling, Simulation, and Reconstruction of 2-Reservoir Heat-to-Power Processes in Finite-Time Thermodynamics
Entropy 2020, 22(9), 997; https://doi.org/10.3390/e22090997 - 07 Sep 2020
Cited by 10 | Viewed by 759
Abstract
The connection between endoreversible models of Finite-Time Thermodynamics and the corresponding real running irreversible processes is investigated by introducing two concepts which complement each other: Simulation and Reconstruction. In that context, the importance of particular machine diagrams for Simulation and (reconstruction) parameter [...] Read more.
The connection between endoreversible models of Finite-Time Thermodynamics and the corresponding real running irreversible processes is investigated by introducing two concepts which complement each other: Simulation and Reconstruction. In that context, the importance of particular machine diagrams for Simulation and (reconstruction) parameter diagrams for Reconstruction is emphasized. Additionally, the treatment of internal irreversibilities through the use of contact quantities like the contact temperature is introduced into the Finite-Time Thermodynamics description of thermal processes. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Averaged Optimization and Finite-Time Thermodynamics
Entropy 2020, 22(9), 912; https://doi.org/10.3390/e22090912 - 20 Aug 2020
Cited by 8 | Viewed by 638
Abstract
The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how [...] Read more.
The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how these problems are linked to the field of finite-time thermodynamics. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Finite-Time Thermodynamics in Economics
Entropy 2020, 22(8), 891; https://doi.org/10.3390/e22080891 - 13 Aug 2020
Cited by 6 | Viewed by 767
Abstract
In this paper, we consider optimal trading processes in economic systems. The analysis is based on accounting for irreversibility factors using the wealth function concept. The existence of the welfare function is proved, the concept of capital dissipation is introduced as a measure [...] Read more.
In this paper, we consider optimal trading processes in economic systems. The analysis is based on accounting for irreversibility factors using the wealth function concept. The existence of the welfare function is proved, the concept of capital dissipation is introduced as a measure of the irreversibility of processes in the microeconomic system, and the economic balances are recorded, including capital dissipation. Problems in the form of kinetic equations leading to given conditions of minimal dissipation are considered. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Re-Optimization of Expansion Work of a Heated Working Fluid with Generalized Radiative Heat Transfer Law
Entropy 2020, 22(7), 720; https://doi.org/10.3390/e22070720 - 29 Jun 2020
Cited by 8 | Viewed by 697
Abstract
Based on the theoretical model of a heated ideal working fluid in the cylinder, the optimal motion path of the piston in this system, for the maximum work output, is re-studied by establishing the changed Lagrangian function and applying the elimination method when [...] Read more.
Based on the theoretical model of a heated ideal working fluid in the cylinder, the optimal motion path of the piston in this system, for the maximum work output, is re-studied by establishing the changed Lagrangian function and applying the elimination method when the initial internal energy, initial volume, finial volume and the process time are given and generalized radiative heat transfer law between the working fluid and heat bath is considered. The analytical solutions of the intermediate Euler-Lagrange arc with square, cubic and radiative heat transfer laws are taken as examples and obtained. The optimal motion path of the piston with cubic heat transfer law, which is obtained by applying the elimination method, is compared with that obtained by applying the Taylor formula expansion method through numerical example. The comparing result shows that the accuracy of the result which is obtained by applying the elimination method is not affected by the length of time of the expansion process of the working fluid, so this result is more universal. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Optimized Piston Motion for an Alpha-Type Stirling Engine
Entropy 2020, 22(6), 700; https://doi.org/10.3390/e22060700 - 23 Jun 2020
Cited by 15 | Viewed by 1017
Abstract
The Stirling engine is one of the most promising devices for the recovery of waste heat. Its power output can be optimized by several means, in particular by an optimized piston motion. Here, we investigate its potential performance improvements in the presence of [...] Read more.
The Stirling engine is one of the most promising devices for the recovery of waste heat. Its power output can be optimized by several means, in particular by an optimized piston motion. Here, we investigate its potential performance improvements in the presence of dissipative processes. In order to ensure the possibility of a technical implementation and the simplicity of the optimization, we restrict the possible piston movements to a parametrized class of smooth piston motions. In this theoretical study the engine model is based on endoreversible thermodynamics, which allows us to incorporate non-equilibrium heat and mass transfer as well as the friction of the piston motion. The regenerator of the Stirling engine is modeled as ideal. An investigation of the impact of the individual loss mechanisms on the resulting optimized motion is carried out for a wide range of parameter values. We find that an optimization within our restricted piston motion class leads to a power gain of about 50% on average. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Article
Endoreversible Models for the Thermodynamics of Computing
Entropy 2020, 22(6), 660; https://doi.org/10.3390/e22060660 - 15 Jun 2020
Cited by 9 | Viewed by 759
Abstract
Landauer’s principle says that, in principle, a computation can be performed without consumption of work, provided no information is erased during the computational process. This principle can be introduced into endoreversible models of thermodynamics. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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Perspective
Use and Abuse of Entropy in Biology: A Case for Caliber
Entropy 2020, 22(12), 1335; https://doi.org/10.3390/e22121335 - 25 Nov 2020
Viewed by 880
Abstract
Here, I discuss entropy and its use as a tool in fields of biology such as bioenergetics, ecology, and evolutionary biology. Statistical entropy concepts including Shannon’s diversity, configurational entropy, and informational entropy are discussed in connection to their use in describing the diversity, [...] Read more.
Here, I discuss entropy and its use as a tool in fields of biology such as bioenergetics, ecology, and evolutionary biology. Statistical entropy concepts including Shannon’s diversity, configurational entropy, and informational entropy are discussed in connection to their use in describing the diversity, heterogeneity, and spatial patterning of biological systems. The use of entropy as a measure of biological complexity is also discussed, and I explore the extension of thermodynamic entropy principles to open, nonequilibrium systems operating in finite time. I conclude with suggestions for use of caliber, a metric similar to entropy but for time-dependent trajectories rather than static distributions, and propose the complementary notion of path information. Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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How It All Began
Entropy 2020, 22(8), 908; https://doi.org/10.3390/e22080908 - 18 Aug 2020
Cited by 6 | Viewed by 1040
Abstract
The first paper published as Finite-Time Thermodynamics is from 1977 [...] Full article
(This article belongs to the Special Issue Finite-Time Thermodynamics)
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