Sampling constraints in average: The example of Hugoniot curves

TL;DR

This paper introduces a stochastic sampling method for microscopic configurations under average constraints, with applications to computing Hugoniot curves in shock physics, supported by convergence proofs.

Contribution

It proposes a novel nonlinear stochastic process for sampling under average constraints and demonstrates its application to Hugoniot curve computation.

Findings

Convergence of the proposed stochastic process is established.

The method effectively computes Hugoniot points for shock-heated materials.

The approach links microscopic sampling with macroscopic physical constraints.

Abstract

We present a method for sampling microscopic configurations of a physical system distributed according to a canonical (Boltzmann-Gibbs) measure, with a constraint holding in average. Assuming that the constraint can be controlled by the volume and/or the temperature of the system, and considering the control parameter as a dynamical variable, a sampling strategy based on a nonlinear stochastic process is proposed. Convergence results for this dynamics are proved using entropy estimates.As an application, we consider the computation of points along the Hugoniot curve, which are equilibrium states obtained after equilibration of a material heated and compressed by a shock wave.