title: Communication: system-size scaling of Boltzmann and alternate Gibbs entropies.
abstract: It has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression S(G)(E) = k ln Σ(E' < E)Ω(E') examined by Gibbs. Here, we show that SG either is equivalent to S in the macroscopic limit or becomes independent of the energy exponentially fast as the system size increases. The resulting exponential scaling makes the realistic use of SG unfeasible and leads in general to temperatures that are inconsistent with the notions of hot and cold.
authors.affiliation: Biophysics Unit (CSIC-UPV/EHU) and Department of Biochemistry and Molecular Biology, University of the Basque Country, P.O. Box 644, 48080 Bilbao, Spain.
authors.forename: Jose M G
authors.initials: JM
authors.lastname: Vilar
authors.affiliation: Departament de Fisica Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain.
authors.forename: J Miguel
authors.initials: JM
authors.lastname: Rubi
mesh_terms: D003080:Cold Temperature; D003198:Computer Simulation; D019277:Entropy; D006358:Hot Temperature; D013816:Thermodynamics