Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-04-05
Phys. Rev. E 72, 026123 (2005)
Physics
Condensed Matter
Statistical Mechanics
13 pages, two columns, 1 figure, RevTex4, version accepted on PRE
Scientific paper
10.1103/PhysRevE.72.026123
It is generally assumed that the thermodynamic stability of equilibrium state is reflected by the concavity of entropy. We inquire, in the microcanonical picture, on the validity of this statement for systems described by the bi-parametric entropy $S_{_{\kappa, r}}$ of Sharma-Taneja-Mittal. We analyze the ``composability'' rule for two statistically independent systems, A and B, described by the entropy $S_{_{\kappa, r}}$ with the same set of the deformed parameters. It is shown that, in spite of the concavity of the entropy, the ``composability'' rule modifies the thermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformed parameters, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})> S_{_{\kappa, r}}({\rm A})+S_{_{\kappa, r}}({\rm B})$ holds (super-additive systems), the concavity conditions does imply the thermodynamics stability. Otherwise, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})
Scarfone Antonio Maria
Wada Takehiko
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