Thermodynamic reduction of contact dynamics

TL;DR

This paper extends a universal algorithm for deriving macroscopic thermodynamic dynamics from microscopic systems to contact Hamiltonian systems, providing a systematic way to obtain thermodynamic invariants and non-equilibrium thermodynamics.

Contribution

It introduces the thermodynamic reduction of contact dynamics, a novel method to derive finite-dimensional non-equilibrium thermodynamic systems from contact Hamiltonian systems.

Findings

Derived a procedure for obtaining dynamical invariants of contact Hamiltonian systems.

Established a method to produce non-equilibrium thermodynamic systems via contact reduction.

Extended the algorithm to contact multi-Hamiltonian systems.

Abstract

A universal algorithm to derive a macroscopic dynamics from the microscopic dynamical system via the averaging process and symplecto-contact reduction was introduced by Jin-wook Lim and the second-named author in [LO23]. They apply the algorithm to derive non-equilibrium thermodynamics from the statistical mechanics utilizing the relative information entropy as a generating function of the associated thermodynamic equilibrium. In the present paper, we apply this algorithm to the contact Hamiltonian dynamical systems. We describe a procedure of obtaining a discrete set of dynamical invariants of the given contact Hamiltonian system, or more generally of a contact multi-Hamiltonian system in a canonical way by deriving a (finite-dimensional non-equilibrium) thermodynamic system. We call this reduction the thermodynamic reduction of contact dynamics.