Fisher Information in Helmholtz-Boltzmann Thermodynamics of Mechanical Systems

In this paper we review Helmholtz-Boltzmann thermodynamics for mechanical systems depending on parameters and we compute the Fisher information matrix for the associated probability density. The divergence of Fisher information has been used as a signal for the existence of phase transitions in finite systems even in the absence of a thermodynamic limit. We investigate through examples if qualitative changes in the dynamic of mechanical systems described by Helmholtz-Boltzmann thermodynamic formalism can be detected using Fisher information.