Strange Lagrangian systems and statistical mechanics

TL;DR

This paper explores how certain particle systems with 'strange' Hamiltonian descriptions exhibit thermodynamic behaviors that differ fundamentally from standard canonical descriptions, highlighting inequivalence in their thermodynamic properties.

Contribution

It demonstrates the thermodynamic inequivalence between strange Hamiltonian systems and standard canonical systems, revealing new insights into their statistical mechanics.

Findings

Strange Hamiltonian systems have thermodynamics differing from canonical systems.

The two descriptions are inequivalent at the thermodynamic level.

Standard and strange descriptions lead to drastically different thermodynamic behaviors.

Abstract

We consider the canonical ensemble of $N$ particles admitting a strange Hamiltonian description. Each of the particles obeys a set of Newtonian equation of motion, which can also be described by the standard canonical Hamiltonian mechanics. However, the thermodynamics corresponding to the strange description and canonical description differ drastically from each other. In other words, the strange description and the standard canonical description are inequivalent on the level of thermodynamics.