Third law of thermodynamics as a key test of generalized entropies

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
E P BentoR Silva

Abstract

The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy S and energy U of an arbitrary N-level classical system. Mathematically, the method relies on exact calculation of β=dS/dU in terms of the microstate probabilities p(i). To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy S(κ), which is additive, and the Tsallis entropy S(q), which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for -1<κ<+1, thereby shedding light on why κ is conventionally restricted to this interval. Surprisingly, however, the Tsallis entropy violates the third law for q<1. Finally, we give a conc...Continue Reading

References

Apr 6, 2001·Physical Review Letters·J A LimaA R Plastino
Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G Kaniadakis
Apr 12, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Michael Nauenberg
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Apr 12, 2006·Physical Review Letters·P DouglasF Renzoni
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Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T S Biró, P Ván
Nov 19, 2013·Physical Review Letters·Steve PresséKen A Dill
Dec 4, 2013·Proceedings of the National Academy of Sciences of the United States of America·Jack PetersonKen A Dill
May 2, 2014·Proceedings of the National Academy of Sciences of the United States of America·Rudolf HanelMurray Gell-Mann

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Citations

Mar 18, 2016·Physical Review. E·G Baris Bagci, Thomas Oikonomou
Jun 18, 2017·Physical Review. E·G KaniadakisT Wada
Nov 19, 2020·Scientific Reports·Giorgio KaniadakisUmberto Lucia
Jun 1, 2018·Entropy·Giorgio Kaniadakis, Dionissios T Hristopulos
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G Baris Bagci, Thomas Oikonomou

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