Nos\'e-Hoover and Langevin thermostats do not reproduce the nonequilibrium behavior of long-range Hamiltonians

TL;DR

This paper demonstrates that Nosé-Hoover and Langevin thermostats cannot accurately replicate the nonequilibrium dynamics of long-range Hamiltonian systems, despite matching equilibrium properties.

Contribution

It reveals the limitations of common thermostats in capturing nonequilibrium behavior in long-range interacting systems.

Findings

Equilibrium properties are correctly reproduced by all methods.

Nosé-Hoover and Langevin thermostats fail to reproduce nonequilibrium dynamics.

The study highlights the need for alternative methods for nonequilibrium simulations.

Abstract

We compare simulations performed using the Nos\'e-Hoover and the Langevin thermostats with the Hamiltonian dynamics of a long-range interacting system in contact with a reservoir. We find that while the statistical mechanics equilibrium properties of the system are recovered by all the different methods, the Nos\'e-Hoover and the Langevin thermostats fail in reproducing the nonequilibrium behavior of such Hamiltonian.