On the logarithmic oscillator as a thermostat

TL;DR

This paper critically examines the logarithmic oscillator as a Hamiltonian thermostat, highlighting theoretical issues that need resolution for effective practical implementation.

Contribution

It provides a detailed analysis of the theoretical limitations of the logarithmic oscillator thermostat proposed by Campisi et al.

Findings

Identifies key theoretical drawbacks of the logarithmic oscillator thermostat

Discusses challenges in practical implementation of this thermostat

Suggests areas for further theoretical development

Abstract

Campisi, Zhan, Talkner and H\"anggi have recently proposed [Campisi] the use of the logarithmic oscillator as an ideal Hamiltonian thermostat, both in simulations and actual experiments. However, the system exhibits several theoretical drawbacks which must be addressed if this thermostat is to be implemented effectively.