Accelerating, to some extent, the $p$-spin dynamics

TL;DR

This paper investigates a non-equilibrium dynamics that violates detailed balance, demonstrating that it accelerates convergence to equilibrium in complex energy landscapes, including disordered p-spin models, during different relaxation stages.

Contribution

It quantifies the speed-up in convergence for systems with complex energy barriers using a detailed-balance violating dynamics, especially in mean-field disordered p-spin models.

Findings

Faster convergence to equilibrium compared to equilibrium dynamics.

Acceleration observed during both β and α relaxation stages.

Provides an interpretation via phase space trajectories and fluctuation-dissipation relations.

Abstract

We consider a detailed-balance violating dynamics whose stationary state is a prescribed Boltzmann distribution. Such dynamics have been shown to be faster than any equilibrium counterpart. We quantify the gain in convergence speed for a system whose energy landscape displays one, and then an infinite number of, energy barriers. In the latter case, we work with the mean-field disordered $p$-spin, and show that the convergence to equilibrium or to the nonergodic phase is accelerated, both during the $\beta$ and $\alpha$-relaxation stages. An interpretation in terms of trajectories in phase space and of an accidental fluctuation-dissipation theorem is provided.