Multihistogram Reweighting for Nonequilibrium Markov Processes Using Sequential Importance Sampling Methods

TL;DR

This paper introduces a multihistogram reweighting technique for nonequilibrium Markov chains, enabling efficient calculation of observable evolution at different parameters based on existing simulation data.

Contribution

It generalizes the multihistogram reweighting method to nonequilibrium Markov processes, expanding its applicability beyond equilibrium systems.

Findings

Improves reweighting range for nonequilibrium simulations

Demonstrates effectiveness on the Ising model with Metropolis dynamics

Applicable to various models and Monte Carlo schemes

Abstract

We present a multihistogram reweighting technique for nonequilibrium Markov Chains with discrete energies. The method generalizes the single histogram method of Yin et al. [Phys. Rev. E72, 036122 (2005)], making it possible to calculate the time evolution of observables at a posteriori chosen couplings based on a set of simulations performed at other couplings. In the same way as multihistogram reweighting in an equilibrium setting improves the practical reweighting range as well as use of available data compared to single histogram reweighting, the method generalizes the multihistogram advantages to nonequilibrium simulations. We demonstrate the procedure for the Ising model with Metropolis dynamics, but stress that the method is generally applicable to a range of models and Monte Carlo update schemes.