A microcanonical entropy correcting finite-size effects in small systems

Year: 2019

Authors: Franzosi R.

Autors Affiliation: QSTAR & CNR—Istituto Nazionale di Ottica, Largo Enrico Fermi 2, I-50125 Firenze, Italy

Abstract: In a recent paper (Franzosi (2018 Physica A 494 302)), we have suggested to use the surface entropy, namely the logarithm of the area of a hypersurface of constant energy in the phase space, as an expression for the thermodynamic microcanonical entropy, in place of the standard definition usually known as Boltzmann entropy. In the present manuscript, we have tested the surface entropy on the Fermi–Pasta–Ulam model for which we have computed the caloric equations that derive from both the Boltzmann entropy and the surface entropy. The results achieved clearly show that in the case of the Boltzmann entropy there is a strong dependence of the caloric equation from the system size, whereas in the case of the surface entropy there is no such dependence. We infer that the issues that one encounters when the Boltzmann entropy is used in the statistical description of small systems could be a clue to a deeper defect of this entropy that derives from its basic definition. Furthermore, we show that the surface entropy is well founded from a mathematical point of view, and we show that it is the only admissible entropy definition, for an isolated and finite system with a given energy, which is consistent with the postulate of equal a priori probability.


Volume: 2019 (8)      Pages from: 083204-1  to: 083204-11

More Information: We acknowledge QuantERA support with the project ?Q-Clocks? and the European Commission.
KeyWords: finite-size scaling, molecular dynamics, microcanonical ensemble
DOI: 10.1088/1742-5468/ab3116

Citations: 4
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