Temperature of a Hamiltonian system given as the effective temperature of a non-equilibrium steady state Langevin thermostat

TL;DR

This paper demonstrates that in non-equilibrium steady states, the kinetic temperature of a Hamiltonian system coupled to a Langevin thermostat equals the effective temperature of the thermostat, strengthening the analogy to equilibrium temperature.

Contribution

It provides evidence that the effective temperature in a non-equilibrium Langevin thermostat corresponds to the kinetic temperature of a coupled Hamiltonian system.

Findings

Kinetic temperature equals the effective temperature of the thermostat.

Supports the analogy between effective temperature and equilibrium temperature.

Enhances understanding of temperature concepts in non-equilibrium systems.

Abstract

In non-equilibrium steady states (NESS) far from equilibrium, it is known that the Einstein relation is violated. Then, the ratio of the diffusion coefficient to the mobility is called an effective temperature, and the physical relevance of this effective temperature has been studied in several works. Although the physical relevance is not yet completely clear, it has been found that the role of an effective temperature in NESS is indeed analogous to that of the temperature in equilibrium systems in a number of respects. In this paper, we find further evidence establishing this analogy. We employ a non-equilibrium Langevin system as a thermostat for a Hamiltonian system and find that the kinetic temperature of this Hamiltonian system is equal to the effective temperature of the thermostat.