A microcanonical entropy correcting finite-size effects in small systems
Autori: Franzosi R.
Affiliazione autori: 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.
Giornale/Rivista: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume: 2019 Da Pagina: 083204-1 A: 083204-11
Parole chiavi: microcanonical ensembleDOI: 10.1088/1742-5468/ab3116Citazioni: 4dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2022-09-25Riferimenti tratti da Isi Web of Knowledge: (solo abbonati) Link per visualizzare la scheda su IsiWeb: Clicca quiLink per visualizzare la citazioni su IsiWeb: Clicca qui