Logarithmic oscillators: ideal Hamiltonian thermostats

TL;DR

Logarithmic oscillators act as ideal Hamiltonian thermostats with infinite heat capacity, enabling the simulation or realization of systems at a fixed temperature through weak coupling, with potential applications in experiments and simulations.

Contribution

This paper introduces logarithmic oscillators as Hamiltonian thermostats that naturally produce Gibbs distributions, bridging theoretical models and experimental implementations.

Findings

Log-oscillators exhibit infinite heat capacity.

Time averages match Gibbs ensemble averages.

Potential for real-world experimental setups.

Abstract

A logarithmic oscillator (in short, log-oscillator) behaves like an ideal thermostat because of its infinite heat capacity: when it weakly couples to another system, time averages of the system observables agree with ensemble averages from a Gibbs distribution with a temperature T that is given by the strength of the logarithmic potential. The resulting equations of motion are Hamiltonian and may be implemented not only in a computer but also with real-world experiments, e.g., with cold atoms.