Impenetrable Barriers in Phase Space for Deterministic Thermostats

TL;DR

This paper explores the phase space structures of deterministic thermostats, revealing that reaction dynamics structures in Hamiltonian systems are preserved in non-Hamiltonian isokinetic thermostatted systems, enabling new analysis methods.

Contribution

It establishes a framework linking Hamiltonian and non-Hamiltonian thermostat phase space structures, facilitating the application of reaction rate theory to thermostat dynamics.

Findings

Phase space structures are preserved between Hamiltonian and non-Hamiltonian systems.

Reaction dynamics concepts apply to thermostatted Hamiltonian systems.

Framework enables new analysis approaches for thermostat behavior.

Abstract

We investigate the relation between the phase space structure of Hamiltonian and non-Hamiltonian deterministic thermostats. We show that phase space structures governing reaction dynamics in Hamiltonian systems map to the same type of phase space structures for the non-Hamiltonian isokinetic equations of motion for the thermostatted Hamiltonian. Our results establish a framework for analyzing thermostat dynamics using concepts and methods developed in reaction rate theory.