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Related papers: Jensen Inequality and the Second Law

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All previously derived thermodynamic fluctuation theorems (FTs) that concern multiple co-evolving systems have required that each system can only change its state during an associated pre-fixed, limited set of time intervals. However, in…

Statistical Mechanics · Physics 2021-04-16 David H. Wolpert

Boltzmann's principle S=k ln W allows to extend equilibrium thermo-statistics to ``Small'' systems without invoking the thermodynamic limit. The clue is to base statistical probability on ensemble averaging and not on time averaging. It is…

Statistical Mechanics · Physics 2007-05-23 D. H. E. Gross

The well known Jensen inequality, holds true for every convex functions. However, we found that it is possible to apply it to some problems related to nonconvex functions for which Jensen's inequality holds true locally. Having considered a…

General Mathematics · Mathematics 2014-12-18 Adilsultan Lepes

Some works have appeared in recent accredited literature considering the possibility of macroscopic violations of the second law in simulated as well as really executed experiments. We argue the inexistence of such violations in experiments…

General Physics · Physics 2018-05-09 Leonardo Chiatti

Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical…

Statistical Mechanics · Physics 2015-05-13 E. M. Sevick , R. Prabhakar , Stephen R. Williams , Debra J. Searles

This article is a short version of a longer article to appear in Physics Reports (cond-mat/9708200). The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of…

Mathematical Physics · Physics 2007-05-23 Elliott H. Lieb , Jakob Yngvason

The possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection…

Statistical Mechanics · Physics 2023-09-07 Andrés Vallejo

We derive a condition for the realizability of heat released in nondeterministic processes from a fluctuation theorem, showing that this condition is strictly stronger than the probabilistic form of the second law of thermodynamics. With…

Statistical Mechanics · Physics 2024-09-26 Jihai Zhu

Quantum thermodynamics investigates how robust the second law of thermodynamics serves as the unique fundamental law in the small quantum world. To tackle this problem, the quantum coherence constitutes a major difficulty of investigations,…

Quantum Physics · Physics 2025-10-08 Naoto Shiraishi , Ryuji Takagi

Statistical physics in equilibrium grants us one of its most powerful tools: the equipartition principle. It states that the degrees of freedom of a mechanical system act as a thermometer: temperature is equal to the mean variance of their…

Statistical Mechanics · Physics 2020-08-26 Alex Fontana , Richard Pedurand , Ludovic Bellon

We consider heat fluctuations and fluctuation theorems for systems driven by multiple reservoirs. We establish a fundamental symmetry obeyed by the joint probability distribution for the heat transfers and system coordinates. The symmetry…

Statistical Mechanics · Physics 2014-10-03 Hans C. Fogedby , Alberto Imparato

Physical devices operating out of equilibrium are inherently affected by thermal fluctuations, limiting their operational precision. This issue is pronounced at microscopic and especially quantum scales and can only be mitigated by…

The Jarzynski equality equates the mean of the exponential of the negative of the work (per fixed temperature) done by a changing Hamiltonian on a system, initially in thermal equilibrium at that temperature, to the ratio of the final to…

High Energy Physics - Theory · Physics 2012-07-17 Don N. Page

Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…

Statistical Mechanics · Physics 2007-09-06 Joel L. Lebowitz

Possible application of a result contradicting to the second law of thermodynamics is announced. According to this result the chaotic energy of thermal fluctuation can be transformed in electric energy of direct current in an inhomogeneous…

General Physics · Physics 2007-05-23 A. V. Nikulov

In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csisz\'{a}r \cite{csi1} $f-$divergence. A result is established that…

Statistics Theory · Mathematics 2007-06-13 Inder Jeet Taneja

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional,…

Biological Physics · Physics 2013-02-01 Sebastien Guenneau , Tania Puvirajesinghe

In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we have addressed the mechanical foundations of equilibrium thermodynamics on the basis of the Generalized Helmholtz Theorem. It was found that the volume entropy…

Statistical Mechanics · Physics 2008-03-09 Michele Campisi

The work is a concept of fundamental importance in thermodynamics. An open question is how to describe the work fluctuation for quantum coherent processes in the presence of initial quantum coherence in the energy basis. With the aim of…

Quantum Physics · Physics 2022-01-05 Gianluca Francica

Jensen's inequality, attributed to Johan Jensen -- a Danish mathematician and engineer noted for his contributions to the theory of functions -- is a ubiquitous result in convex analysis, providing a fundamental lower bound for the…

Information Theory · Computer Science 2026-01-09 Sambhab Mishra