Hamiltonian thermodynamics

TL;DR

This paper demonstrates that deterministic Hamiltonian systems can be described using thermodynamic concepts like energy, temperature, and entropy, with laws and cycles analogous to traditional thermodynamics.

Contribution

It introduces a thermodynamic-like framework for Hamiltonian systems, establishing laws and concepts typically associated with stochastic systems.

Findings

Thermodynamic relations are rigorously derived for Hamiltonian systems.

Concepts of thermodynamic state, process, and cycle are applicable to deterministic systems.

Analogues of thermodynamic laws hold in Hamiltonian dynamics.

Abstract

It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the considered Hamiltonian systems, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.