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It is shown that Onsager's principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is…

Statistical Mechanics · Physics 2015-05-18 Pasko Zupanovic , Domagoj Kuic , Zeljana Bonacic Losic , Drazen Petrov , Davor Juretic , Milan Brumen

We propose a method for inferring entropy production (EP) in high-dimensional stochastic systems, including many-body systems and non-Markovian systems with long memory. Standard techniques for estimating EP become intractable in such…

Statistical Mechanics · Physics 2026-02-20 Miguel Aguilera , Sosuke Ito , Artemy Kolchinsky

The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state are considered. While for stationary states with a constant kinetic energy the two rates…

Statistical Mechanics · Physics 2009-10-30 E. G. D. Cohen , L. Rondoni

To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…

Statistical Mechanics · Physics 2007-05-23 V. V. Ryazanov , S. G. Shpyrko

By employing a path integral formulation, we obtain the entropy production rate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the presence and in the absence of thermal noise. The present treatment clarifies some…

Statistical Mechanics · Physics 2019-09-04 Lorenzo Caprini , Umberto Marini Bettolo Marconi , Andrea Puglisi , Angelo Vulpiani

Work fluctuation and total entropy production play crucial roles in small thermodynamic systems subject to large thermal fluctuations. We investigate a trade-off relation between them in a nonequilibrium situation in which a system starts…

Statistical Mechanics · Physics 2016-12-15 Ken Funo , Tomohiro Shitara , Masahito Ueda

We study hydrodynamics coupled to order parameter based on linear sigma model. We obtain numerical solutions for both boost invariant and non-boost invariant solutions. Both solutions show the order parameter rises with oscillations, which…

Nuclear Theory · Physics 2020-04-24 Shu Lin , Gezheng Zhou

We investigate the possible thermalization process of the highly occupied and weakly coupled Yang-Mills fields expanding along the beam axis through an evaluation of the entropy, particle number, and pressure anisotropy. The time evolution…

High Energy Physics - Phenomenology · Physics 2022-06-08 Hidefumi Matsuda , Teiji Kunihiro , Akira Ohnishi , Toru T. Takahashi

Biological and engineered systems operate by coupling function to the transfer of heat and/or particles down a thermal or chemical gradient. In idealized \textit{deterministically} driven systems, thermodynamic control can be exerted…

Statistical Mechanics · Physics 2016-01-06 Benjamin B. Machta

Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the…

Statistical Mechanics · Physics 2017-04-26 Cesare Nardini , Etienne Fodor , Elsen Tjhung , Frederic van Wijland , Julien Tailleur , Michael E. Cates

From a new rigorous formulation of the general axiomatic foundations of thermodynamics we derive an operational definition of entropy that responds to the emergent need in many technological frameworks to understand and deploy thermodynamic…

Quantum Physics · Physics 2019-11-21 Gian Paolo Beretta , Enzo Zanchini

The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…

Soft Condensed Matter · Physics 2025-05-15 Robin Bebon , Joshua F. Robinson , Thomas Speck

One of the key objectives in investigating small stochastic systems is the development of micrometer-sized engines and the understanding of their thermodynamics. However, the primary mathematical tool used for this purpose, the overdamped…

Statistical Mechanics · Physics 2025-03-31 Shakul Awasthi , Hyunggyu Park , Jae Sung Lee

Recently, the fundamental laws of thermodynamics have been reconsidered for small systems. The discovery of the fluctuation relations has spurred theoretical and experimental studies on thermodynamics of systems with few degrees of freedom.…

Statistical Mechanics · Physics 2021-08-10 J. V. Koski , T. Sagawa , O. -P. Saira , Y. Yoon , A. Kutvonen , P. Solinas , M. Möttönen , T. Ala-Nissila , J. P. Pekola

We consider a quantum spin system consisting of a finite subsystem connected to infinite reservoirs at different temperatures. In this setup we define nonequilibrium steady states and prove that the rate of entropy production in such states…

Mathematical Physics · Physics 2009-10-31 David Ruelle

We study thermodynamic processes in contact with a heat bath that may have an arbitrary time-varying periodic temperature profile. Within the framework of stochastic thermodynamics, and for models of thermo-dynamic engines in the idealized…

Optimization and Control · Mathematics 2022-04-06 Olga Movilla Miangolarra , Rui Fu , Amirhossein Taghvaei , Yongxin Chen , Tryphon T. Georgiou

Entropy production of an active particle in an external potential is identified through a thermodynamically consistent minimal lattice model that includes the chemical reaction providing the propulsion and ordinary translational noise. In…

Statistical Mechanics · Physics 2017-12-01 Patrick Pietzonka , Udo Seifert

The connection between the rate of entropy production and the rate of phase space contraction for thermostatted systems in nonequilibrium steady states is discussed for a simple model of heat flow in a Lorentz gas, previously described by…

Chaotic Dynamics · Physics 2009-10-31 Henk van Beijeren , J. R. Dorfman

Entropy production (EP) is a central measure in nonequilibrium thermodynamics, as it can quantify the irreversibility of a process as well as its energy dissipation in special cases. Using the time-reversal asymmetry in a system's path…

Statistical Mechanics · Physics 2022-04-26 Dong-Kyum Kim , Sangyun Lee , Hawoong Jeong

We address the emergence of entropy production in the non-equilibrium process of an open quantum system from the viewpoint of the environment. By making use of a dilation-based approach akin to Stinespring theorem, we derive an expression…