In an 1884 paper, Boltzmann showed that for a one-dimensional mechanical system with a convex potential energy phi that depends on a parameter V, it is possible to define a temperature T, pressure p, and entropy S that satisfy the Gibbs relation TdS = de + p dV, where e = kin.en+phi. In the paper we review the extension of the Boltzmann construction to general natural mechanical systems endowed with a fibration over the (possibly multidimensional) space of macroscopic parameters. Moreover, for certain discrete mechanical systems with non-convex potential energies, which are used as models for phase transitions in solids, we compare the thermodynamic pressure p = p(e,V) introduced above with the quasi-static, macroscopic, stress-strain relation.

Helmholtz-Boltzmann thermodynamics on Configurations Space

CARDIN, FRANCO;FAVRETTI, MARCO
2002

Abstract

In an 1884 paper, Boltzmann showed that for a one-dimensional mechanical system with a convex potential energy phi that depends on a parameter V, it is possible to define a temperature T, pressure p, and entropy S that satisfy the Gibbs relation TdS = de + p dV, where e = kin.en+phi. In the paper we review the extension of the Boltzmann construction to general natural mechanical systems endowed with a fibration over the (possibly multidimensional) space of macroscopic parameters. Moreover, for certain discrete mechanical systems with non-convex potential energies, which are used as models for phase transitions in solids, we compare the thermodynamic pressure p = p(e,V) introduced above with the quasi-static, macroscopic, stress-strain relation.
2002
Proceedings "Wascom 2001" 11th Conference on Waves and Stability in Continuous Media
9789812380173
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1339751
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