Entropy

Editorial

Jump to: Research

3 pages, 515 KiB

Open AccessEditorial

Maximum Power Efficiency

by Boye Ahlborn and Frank Curzon

Entropy 2025, 27(7), 714; https://doi.org/10.3390/e27070714 - 1 Jul 2025

Viewed by 233

Abstract

New research often starts with vague, dream-like ideas, conversed on over coffee in the free flow of animated discussions about physics, the growing up of one’s children, politics, and the success of the local ice hockey team [...] Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

Research

Jump to: Editorial

15 pages, 847 KiB

Open AccessArticle

Compressor Power and Efficiency Optimization: A Finite-Time Thermodynamics Approach

by François Lanzetta

Entropy 2025, 27(8), 842; https://doi.org/10.3390/e27080842 - 8 Aug 2025

Viewed by 106

Abstract

This paper presents a theoretical optimization of an endoreversible compressor under steady-state conditions. A parametric study using finite-time thermodynamic principles highlights the effect of external irreversibilities on compressor performance. A compressor efficiency metric is established based on heat pump theory’s analogous performance coefficient [...] Read more.

This paper presents a theoretical optimization of an endoreversible compressor under steady-state conditions. A parametric study using finite-time thermodynamic principles highlights the effect of external irreversibilities on compressor performance. A compressor efficiency metric is established based on heat pump theory’s analogous performance coefficient concept. The external irreversibilities are characterized as functions of the conductance coefficients between the compressor and the low- and high-pressure reservoirs. In particular, the influence of suction and discharge tube diameters and gas pressures is investigated to determine the optimum compressor operating performance for a given gas mass flow rate. The results highlight the importance of selecting optimal suction and discharge tube diameters to improve compressor power efficiency and minimize energy consumption during gas compression. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Figure 1

24 pages, 9086 KiB

Open AccessArticle

Linking Optimization Success and Stability of Finite-Time Thermodynamics Heat Engines

by Julian Gonzalez-Ayala, David Pérez-Gallego, Alejandro Medina, José M. Mateos Roco, Antonio Calvo Hernández, Santiago Velasco and Fernando Angulo-Brown

Entropy 2025, 27(8), 822; https://doi.org/10.3390/e27080822 - 2 Aug 2025

Viewed by 228

Abstract

In celebration of 50 years of the endoreversible Carnot-like heat engine, this work aims to link the thermodynamic success of the irreversible Carnot-like heat engine with the stability dynamics of the engine. This region of success is defined by two extreme configurations in [...] Read more.

In celebration of 50 years of the endoreversible Carnot-like heat engine, this work aims to link the thermodynamic success of the irreversible Carnot-like heat engine with the stability dynamics of the engine. This region of success is defined by two extreme configurations in the interaction between heat reservoirs and the working fluid. The first corresponds to a fully reversible limit, and the second one is the fully dissipative limit; in between both limits, the heat exchange between reservoirs and working fluid produces irreversibilities and entropy generation. The distance between these two extremal configurations is minimized, independently of the chosen metric, in the state where the efficiency is half the Carnot efficiency. This boundary encloses the region where irreversibilities dominate or the reversible behavior dominates (region of success). A general stability dynamics is proposed based on the endoreversible nature of the model and the operation parameter in charge of defining the operation regime. For this purpose, the maximum ecological and maximum Omega regimes are considered. The results show that for single perturbations, the dynamics rapidly directs the system towards the success region, and under random perturbations producing stochastic trajectories, the system remains always in this region. The results are contrasted with the case in which no restitution dynamics exist. It is shown that stability allows the system to depart from the original steady state to other states that enhance the system’s performance, which could favor the evolution and specialization of systems in nature and in artificial devices. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Figure 1

40 pages, 585 KiB

Open AccessArticle

Finite-Time Thermodynamics and Complex Energy Landscapes: A Perspective

by Johann Christian Schön

Entropy 2025, 27(8), 819; https://doi.org/10.3390/e27080819 - 1 Aug 2025

Viewed by 193

Abstract

Finite-time thermodynamics (FTT) describes the study of thermodynamic processes that take place in finite time. Due to the finite-time requirement, in general the system cannot move from equilibrium state to equilibrium state. As a consequence, excess entropy is generated, available work is reduced, [...] Read more.

Finite-time thermodynamics (FTT) describes the study of thermodynamic processes that take place in finite time. Due to the finite-time requirement, in general the system cannot move from equilibrium state to equilibrium state. As a consequence, excess entropy is generated, available work is reduced, and/or the maximally achievable efficiency is not achieved; minimizing these negative side-effects constitutes an optimal control problem. Particularly challenging are processes and cycles that involve phase transitions of the working fluid material or the target material of a synthesis process, especially since most materials reside on a highly complex energy landscape exhibiting alternative metastable phases or glassy states. In this perspective, we discuss the issues and challenges involved in dealing with such materials when performing thermodynamic processes that include phase transitions in finite time. We focus on thermodynamic cycles with one back-and-forth transition and the generation of new materials via a phase transition; other systems discussed concern the computation of free energy differences and the general applicability of FTT to systems outside the realm of chemistry and physics that exhibit cost function landscapes with phase transition-like dynamics. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Figure 1

11 pages, 343 KiB

Open AccessArticle

Endoreversible Stirling Cycles: Plasma Engines at Maximal Power

by Gregory Behrendt and Sebastian Deffner

Entropy 2025, 27(8), 807; https://doi.org/10.3390/e27080807 - 28 Jul 2025

Viewed by 558

Abstract

Endoreversible engine cycles are a cornerstone of finite-time thermodynamics. We show that endoreversible Stirling engines operating with a one-component plasma as a working medium run at maximal power output with the Curzon–Ahlborn efficiency. As a main result, we elucidate that this is actually [...] Read more.

Endoreversible engine cycles are a cornerstone of finite-time thermodynamics. We show that endoreversible Stirling engines operating with a one-component plasma as a working medium run at maximal power output with the Curzon–Ahlborn efficiency. As a main result, we elucidate that this is actually a consequence of the fact that the caloric equation of state depends only linearly on temperature and only additively on volume. In particular, neither the exact form of the mechanical equation of state nor the full fundamental relation are required. Thus, our findings immediately generalize to a larger class of working plasmas, far beyond simple ideal gases. In addition, we show that for plasmas described by the photonic equation of state, the efficiency is significantly lower. This is in stark contrast to endoreversible Otto cycles, for which photonic engines have an efficiency larger than the Curzon–Ahlborn efficiency. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Figure 1

19 pages, 994 KiB

Open AccessArticle

(Finite-Time) Thermodynamics, Hyperbolicity, Lorentz Invariance: Study of an Example

by Bernard Guy

Entropy 2025, 27(7), 700; https://doi.org/10.3390/e27070700 - 29 Jun 2025

Viewed by 397

Abstract

Our study lies at the intersection of three fields: finite-time thermodynamics, relativity theory, and the theory of hyperbolic conservation laws. Each of these fields has its own requirements and richness, and in order to link them together as effectively as possible, we have [...] Read more.

Our study lies at the intersection of three fields: finite-time thermodynamics, relativity theory, and the theory of hyperbolic conservation laws. Each of these fields has its own requirements and richness, and in order to link them together as effectively as possible, we have simplified each one, reducing it to its fundamental principles. The example chosen concerns the propagation of chemical changes in a very large reactor, as found in geology. We ask ourselves two sets of questions: (1) How do the finiteness of propagation speeds modeled by hyperbolic problems (diffusion is neglected) and the finiteness of the time allocated to transformations interact? (2) How do the finiteness of time and that of resources interact? The similarity in the behavior of the pairs of variables (x, t and resources, resource flows) in Lorentz relativistic transformations allows us to put them on the same level and propose complementary-type relationships between the two classes of finiteness. If times are finite, so are resources, which can be neither zero nor infinite. In hyperbolic problems, a condition is necessary to select solutions with a physical sense among the multiplicity of weak solutions: this is given by the entropy production, which is Lorentz invariant (and not entropy alone). Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Figure 1

26 pages, 328 KiB

Open AccessFeature PaperArticle

Finite-Time Thermodynamics: Problems, Approaches, and Results

by Anatoly M. Tsirlin, Alexander I. Balunov and Ivan A. Sukin

Entropy 2025, 27(6), 649; https://doi.org/10.3390/e27060649 - 17 Jun 2025

Viewed by 341

Abstract

In this manuscript, the typical problems of “finite-time thermodynamics”, their general methodology, and the general features of their solutions are considered. We also consider the role of minimal dissipation processes, the properties of the irreversibility index, and the consequences of its existence. A [...] Read more.

In this manuscript, the typical problems of “finite-time thermodynamics”, their general methodology, and the general features of their solutions are considered. We also consider the role of minimal dissipation processes, the properties of the irreversibility index, and the consequences of its existence. A generalization of the Carathéodory theorem for averaged optimization problems corresponding to cyclic processes and the properties of optimal solutions following from it are given. The existence of the irreversibility index for economic macrosystems and their analogies to and differences from thermodynamic systems are proven. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Figure 1

11 pages, 1908 KiB

Open AccessArticle

Thermodynamics of Intrinsic Reaction Coordinate (IRC) Chemical Reaction Pathways

by Frank Weinhold

Entropy 2025, 27(4), 390; https://doi.org/10.3390/e27040390 - 7 Apr 2025

Cited by 2 | Viewed by 796

Abstract

We address the scientific “time” concept in the context of more general relaxation processes toward the Wärmetod of thermodynamic equilibrium. More specifically, we sketch a construction of a conceptual ladder of chemical reaction steps that can rigorously bridge a description from the microscopic [...] Read more.

We address the scientific “time” concept in the context of more general relaxation processes toward the Wärmetod of thermodynamic equilibrium. More specifically, we sketch a construction of a conceptual ladder of chemical reaction steps that can rigorously bridge a description from the microscopic domain of molecular quantum chemistry to the macroscopic materials domain of Gibbsian thermodynamics. This conceptual reformulation follows the pioneering work of Kenichi Fukui (Nobel 1981) in rigorously formulating the intrinsic reaction coordinate (IRC) pathway for controlled description of non-equilibrium passages between reactant and product equilibrium states of an overall material transformation. Elementary chemical reaction steps are thereby identified as the logical building-blocks of an integrated mathematical framework that seamlessly spans the gulf between classical (pre-1925) and quantal (post-1925) scientific conceptions and encompasses both static and dynamic aspects of material change. All modern chemical reaction rate studies build on the apparent infallibility of quantum-chemical solutions of Schrödinger’s wave equation and its Dirac-type relativistic corrections. This infallibility may now be properly accepted as an added“inductive law” of Gibbsian chemical thermodynamics, the only component of 19th-century physics that passed intact through the revolutionary quantum upheavals of 1925. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Graphical abstract

10 pages, 448 KiB

Open AccessArticle

Revisiting Endoreversible Carnot Engine: Extending the Yvon Engine

by Xiu-Hua Zhao and Yu-Han Ma

Entropy 2025, 27(2), 195; https://doi.org/10.3390/e27020195 - 13 Feb 2025

Cited by 1 | Viewed by 1088

Abstract

Curzon and Ahlborn’s 1975 paper, a pioneering work that inspired the birth of the field of finite-time thermodynamics, unveiled the efficiency at maximum power (EMP) of the endoreversible Carnot heat engine, now commonly referred to as the Curzon–Ahlborn (CA) engine. Historically, despite the [...] Read more.

Curzon and Ahlborn’s 1975 paper, a pioneering work that inspired the birth of the field of finite-time thermodynamics, unveiled the efficiency at maximum power (EMP) of the endoreversible Carnot heat engine, now commonly referred to as the Curzon–Ahlborn (CA) engine. Historically, despite the significance of the CA engine, similar findings had emerged at an earlier time, such as the Yvon engine proposed by J. Yvon in 1955 that shares the exact same EMP, that is, the CA efficiency

η_{CA}

. However, the special setup of the Yvon engine has circumscribed its broader influence. This paper extends the Yvon engine model to achieve a level of generality comparable to that of the CA engine. With the power expression of the extended Yvon engine, we directly explain the universality that

η_{CA}

is independent of the heat transfer coefficients between the working substance and the heat reservoirs. A rigorous comparison reveals that the extended Yvon engine and CA engine represent the steady-state and cyclic forms of the endoreversible Carnot heat engine, respectively, and are equivalent. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

► Show Figures

Figure 1

Journal Menu

Journal Browser

The First Half Century of Finite-Time Thermodynamics

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Related Special Issue

Published Papers (9 papers)

Editorial

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI