Frictionless thermostats and intensive constants of motion

TL;DR

This paper demonstrates that in space-dimension thermostats models for nonequilibrium statistical mechanics, the thermodynamic limit reveals infinitely many conserved quantities called intensive observables.

Contribution

It introduces the concept that thermostats models in various dimensions possess infinitely many constants of motion in the thermodynamic limit, highlighting a new aspect of their dynamical structure.

Findings

Infinitely many constants of motion exist in the thermodynamic limit.

Intensive observables serve as conserved quantities.

The results apply to models in space dimensions 1, 2, and 3.

Abstract

Thermostats models in space dimension d=1,2,3 for nonequilibrium statistical mechanics are considered and it is shown that, in the thermodynamic limit, the evolutions admit infinitely many constants of motion: namely the intensive observables.