A thermostat algorithm generating target ensembles

TL;DR

This paper introduces a deterministic contact density dynamics algorithm that generates specific target distributions in phase space, extending previous methods like Nosé-Hoover with a contact geometry framework.

Contribution

The paper presents a novel contact geometry-based algorithm for generating prescribed phase space distributions, generalizing existing thermostat methods.

Findings

Successfully generates Gibbs distribution for a harmonic oscillator

Demonstrates the algorithm's ability to produce arbitrary target distributions

Shows the equations of motion resemble those of density dynamics

Abstract

We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nos\'e-Hoover, our algorithm is based on a non-Hamiltonian system in an extended phase space. However the equations of motion in our case follow from contact geometry and we show that in general they have a similar form to those of the so-called density dynamics algorithm. As a prototypical example, we apply our algorithm to produce Gibbs canonical distribution for a one-dimensional harmonic oscillator.