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The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy…

Soft Condensed Matter · Physics 2009-10-30 Elliott H. Lieb , Jakob Yngvason

During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…

Statistical Mechanics · Physics 2009-11-07 Michael Nauenberg

The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic…

Statistical Mechanics · Physics 2009-10-31 Sumiyoshi Abe , S. Martinez , F. Pennini , A. Plastino

This review presents the effective temperature notion as defined from the deviations from the equilibrium fluctuation-dissipation theorem in out of equilibrium systems with slow dynamics. The thermodynamic meaning of this quantity is…

Statistical Mechanics · Physics 2015-05-28 Leticia F. Cugliandolo

Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…

Quantum Physics · Physics 2026-03-26 Gian Paolo Beretta

Classical thermodynamics treats temperature as a state variable characterizing systems in equilibrium with idealized infinite reservoirs. We argue that this framing, while computationally exact, obscures an essential physical reality: any…

Quantum Physics · Physics 2026-04-14 David Vaknin

Recently, a thermodynamic definition of time has been introduced. This definition is useful to find approach some open problems in physics. But, it was obtained by a phenomenological approach and a logical inconsistency appears in the…

Statistical Mechanics · Physics 2023-11-14 Umberto Lucia

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

Considering an entropy-based division of energy transferred into heat and work, we develop an alternative theoretical framework for the thermodynamic analysis of two-level systems. When comparing these results with those obtained under the…

Quantum Physics · Physics 2021-04-14 Andrés Vallejo , Alejandro Romanelli , Raúl Donangelo

This paper is a non-technical, informal presentation of our theory of the second law of thermodynamics as a law that is independent of statistical mechanics and that is derivable solely from certain simple assumptions about adiabatic…

Mathematical Physics · Physics 2009-10-31 Elliott H. Lieb , Jakob Yngvason

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by…

Statistical Mechanics · Physics 2008-04-15 V. Garcia-Morales , J. Pellicer , J. A. Manzanares

The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We invent a concrete…

Statistical Mechanics · Physics 2007-05-23 Takahiro Hatano , David Jou

We extend the Carath\'{e}odory principle of the Second Law to quantum thermodynamics with energy levels depending on macroscopic variables, such as volume and magnetic field. This extension introduces the concept of Quantum Thermodynamic…

Statistical Mechanics · Physics 2025-09-09 Ruo-Xun Zhai , C. P. Sun

The existence of fluctuations of temperature has been a somewhat controversial topic in thermodynamics but nowadays it is recognized that they must be taken into account in small, finite systems. Although for nonequilibrium steady states…

Statistical Mechanics · Physics 2022-01-05 Sergio Davis

An explicit expression for the temperature of an open two-level quantum system is obtained as a function of local properties, under the hypothesis of weak interaction with the environment. This temperature is defined for both equilibrium…

Quantum Physics · Physics 2020-05-20 Andrés Vallejo , Alejandro Romanelli , Raúl Donangelo

In this paper we develop a generalized formalism for equilibrium thermodynamic systems when an information is shared between the system and the reservoir. The information results in a correction to the entropy of the system. This extension…

Statistical Mechanics · Physics 2013-05-10 Alessio Gagliardi , Aldo Di Carlo

Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention.…

Statistical Mechanics · Physics 2026-04-21 Sergio Davis

Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It…

Statistical Mechanics · Physics 2011-11-10 Gavin E. Crooks

The notion of configuration temperature is extended to discontinuous systems by identifying the temperature as the nontrivial root of several integral equations regarding the distribution of the energy change upon configuration…

Statistical Mechanics · Physics 2013-03-26 Cheng Zhang

The time-dependence of the quantum entropy for a two-level atom interacting with a single-cavity mode is computed using the Jaynes-Cummings model, when the initial state of the radiation field is prepared in a thermal state with temperature…

Quantum Physics · Physics 2022-01-26 Jorge David Castaño-Yepes