On the Helmholtz-Boltzmann thermodynamics of mechanical systems

F. Cardin; M. Favretti
February 2004
Continuum Mechanics & Thermodynamics;Feb2004, Vol. 16 Issue 1/2, p15
Academic Journal
In an 1884 paper, Boltzmann showed that for a one-dimensional mechanical system with a convex potential energy $\varphi$ that depends on a parameter V, it is possible to define a temperature T, pressure p, and entropy S that satisfy the Gibbs relation Td S = d e + p d V, where $e = \mathrm{kin. en.} + \varphi$ . 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.


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