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Entropy
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Nonequilibrium Thermodynamics and Stochastic Processes
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Nonequilibrium Thermodynamics and Stochastic Processes

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

Deadline for manuscript submissions: closed (20 March 2022) | Viewed by 19744

Special Issue Editor

Dr. Henni Ouerdane

E-Mail Website
Guest Editor
Skolkovo Institute of Science and Technology, 30 Bolshoi Boulevard, bld. 1, Moscow 121205, Russia
Interests: nonequilibrium thermodynamics; energy conversion; energy systems; condensed matter physics; quantum technologies
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As it did for classical thermodynamics, a phenomenological approach drove the development of nonequilibrium thermodynamics, at the heart of which lie the local equilibrium assumption and the minimum entropy production hypothesis. Linear response theory, which specializes in close-to-equilibrium problems, constitutes an important milestone as it provides deep insights into the actual physical processes at work and their rates during the evolution of natural and artificial systems. Extending the scope of nonequilibrium thermodynamics to systems far from equilibrium still is an open challenge. Development of stochastic thermodynamics is a decisive progress as it provides a framework where key classical thermodynamic concepts, heat, work and entropy, find a definition at the level of individual trajectories pertinent notably to small-scale, far from equilibrium systems. Quantum thermodynamics constitutes also an active front of research: open quantum dynamics, coherence and dissipation at the quantum level can contribute to the fundamental base upon which equilibrium and nonequilibrium thermodynamics would rest, and from which the first and second laws would naturally emerge. Last, but perhaps not least, machine learning may also reveal itself as a powerful tool to gain unprecedented insight into the nonequilibrium properties of any complex system, both close and far from equilibrium, and undergoing phase transitions. 

This Special Issue aims to gather articles which will cover a wide range of systems and problems pertaining to nonequilibrium and stochastic thermodynamics and will provide a unifying vision of the field underpinned by entropy and information theory. It is anticipated that contributions will essentially contain theoretical developments, but submission of manuscripts reporting basic experimental results analyzed in the frame of theories pertinent to the Special Issue, as well as those discussing emerging technologies derived from nonequilibrium and stochastic thermodynamics are particularly welcome.

Prof. Dr. Henni Ouerdane
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Energy conversion, including thermoelectric, electrochemical, chemical reactions, etc. 
  • Self-organization 
  • Classical and quantum dissipative systems 
  • Mesoscopic systems 
  • Stochastic thermodynamics: MEMS, molecular motors, colloids, biomolecules 
  • Non-Markovian dynamics 
  • Fluctuation theorems 
  • Open quantum systems 
  • Quantum thermodynamics 
  • Machine learning methods

Published Papers (5 papers)

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Research

31 pages, 668 KiB  
Article
Quantum Heat Engines with Complex Working Media, Complete Otto Cycles and Heuristics
by Ramandeep S. Johal and Venu Mehta
Entropy 2021, 23(9), 1149; https://doi.org/10.3390/e23091149 - 01 Sep 2021
Cited by 9 | Viewed by 2585
Abstract
Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to [...] Read more.
Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance. Full article
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Stochastic Processes)
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29 pages, 28185 KiB  
Article
The Problem of Engines in Statistical Physics
by Robert Alicki, David Gelbwaser-Klimovsky and Alejandro Jenkins
Entropy 2021, 23(8), 1095; https://doi.org/10.3390/e23081095 - 22 Aug 2021
Cited by 3 | Viewed by 4068
Abstract
Engines are open systems that can generate work cyclically at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their dynamics in time a [...] Read more.
Engines are open systems that can generate work cyclically at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their dynamics in time a theoretical blind spot. This has hampered the usefulness of statistical mechanics applied to active systems, including living matter. We argue that recent advances in the theory of open quantum systems, coupled with renewed interest in understanding how active forces result from positive feedback between different macroscopic degrees of freedom in the presence of dissipation, point to a more realistic description of autonomous engines. We propose a general conceptualization of an engine that helps clarify the distinction between its heat and work outputs. Based on this, we show how the external loading force and the thermal noise may be incorporated into the relevant equations of motion. This modifies the usual Fokker–Planck and Langevin equations, offering a thermodynamically complete formulation of the irreversible dynamics of simple oscillating and rotating engines. Full article
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Stochastic Processes)
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14 pages, 4771 KiB  
Article
Dissipation-Driven Selection under Finite Diffusion: Hints from Equilibrium and Separation of Time Scales
by Shiling Liang, Paolo De Los Rios and Daniel Maria Busiello
Entropy 2021, 23(8), 1068; https://doi.org/10.3390/e23081068 - 17 Aug 2021
Cited by 1 | Viewed by 2326
Abstract
When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available energy, might be dominant in dictating the [...] Read more.
When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available energy, might be dominant in dictating the stationary populations of all chemical states out of equilibrium. This phenomenology has been theoretically explored mainly in the infinite diffusion limit. Here, we show that the regime in which the diffusion rate is finite, and also slower than some chemical reactions, might bring about interesting features, such as the maximisation of selection or the switch of the selected state at stationarity. We introduce a framework, rooted in a time-scale separation analysis, which is able to capture leading non-equilibrium features using only equilibrium arguments under well-defined conditions. In particular, it is possible to identify fast-dissipation sub-networks of reactions whose Boltzmann equilibrium dominates the steady-state of the entire system as a whole. Finally, we also show that the dissipated heat (and so the entropy production) can be estimated, under some approximations, through the heat capacity of fast-dissipation sub-networks. This work provides a tool to develop an intuitive equilibrium-based grasp on complex non-isothermal reaction networks, which are important paradigms to understand the emergence of complex structures from basic building blocks. Full article
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Stochastic Processes)
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25 pages, 6027 KiB  
Article
Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay
by Sarah A. M. Loos, Simon Hermann and Sabine H. L. Klapp
Entropy 2021, 23(6), 696; https://doi.org/10.3390/e23060696 - 31 May 2021
Cited by 3 | Viewed by 3673
Abstract
Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed [...] Read more.
Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system’s linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback. Full article
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Stochastic Processes)
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33 pages, 586 KiB  
Article
Entropy Production in Exactly Solvable Systems
by Luca Cocconi, Rosalba Garcia-Millan, Zigan Zhen, Bianca Buturca and Gunnar Pruessner
Entropy 2020, 22(11), 1252; https://doi.org/10.3390/e22111252 - 03 Nov 2020
Cited by 26 | Viewed by 5446
Abstract
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and [...] Read more.
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms. Full article
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Stochastic Processes)
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