Comment on "Logarithmic Oscillators: Ideal Hamiltonian Thermostats" [arXiv 1203.5968]

TL;DR

This paper critically examines a proposed Hamiltonian thermostat based on logarithmic oscillators, demonstrating that practical implementation is infeasible due to exponentially large time and length scales, making equilibration impossible within realistic timeframes.

Contribution

The authors provide a critical analysis showing that the proposed thermostat cannot be practically implemented because of exponential scaling of time and length scales with system energy.

Findings

Implementation requires equilibration times exceeding the universe's age for systems with more than a few dozen particles.

Logarithmic oscillator thermostats are not feasible for realistic simulations or experiments.

Exponential dependence on energy makes the proposed thermostat impractical for larger systems.

Abstract

Campisi, Zhan, Talkner and H\"anggi have recently proposed a novel Hamiltonian thermostat which they claim may be used both in simulations and experiments [arXiv:1203.5968v4]. We show, however, that this is not possible due to the length and time scales involved, which depend exponentially on the total energy of the system. The implementation suggested by Campisi et alii implies equilibration times greater than the age of the universe for systems with more than a few dozen particles.