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Entropy 2014, 16(3), 1547-1570;

Recent Progress in the Definition of Thermodynamic Entropy

Department of Industrial Engineering, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy
Author to whom correspondence should be addressed.
Received: 2 January 2014 / Revised: 17 February 2014 / Accepted: 12 March 2014 / Published: 19 March 2014
(This article belongs to the Special Issue Advances in Methods and Foundations of Non-Equilibrium Thermodynamics)
Full-Text   |   PDF [293 KB, uploaded 24 February 2015]


The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carathéodory, the Keenan School, Lieb and Yngvason, and the present authors. An improvement of the latter method is then presented. Seven basic axioms are employed: three Postulates, which are considered as having a quite general validity, and four Assumptions, which identify the domains of validity of the definitions of energy (Assumption 1) and entropy (Assumptions 2, 3, 4). The domain of validity of the present definition of entropy is not restricted to stable equilibrium states. For collections of simple systems, it coincides with that of the proof of existence and uniqueness of an entropy function which characterizes the relation of adiabatic accessibility proposed by Lieb and Yngvason. However, our treatment does not require the formation of scaled copies so that it applies not only to collections of simple systems, but also to systems contained in electric or magnetic fields and to small and few-particle systems. View Full-Text
Keywords: entropy; operational definition; nonequilibrium states; non-simple systems entropy; operational definition; nonequilibrium states; non-simple systems
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Zanchini, E.; Beretta, G.P. Recent Progress in the Definition of Thermodynamic Entropy. Entropy 2014, 16, 1547-1570.

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