Acceleration effect caused by the Onsager reaction term in a frustrated coupled oscillator system

TL;DR

This paper investigates how the Onsager reaction term (ORT) causes an acceleration effect in frustrated coupled oscillator systems, revealing a unique non-equilibrium phenomenon not present in equilibrium systems.

Contribution

It demonstrates that the ORT induces an acceleration effect in non-equilibrium oscillator models, a phenomenon absent in equilibrium systems, and compares symmetric and asymmetric coupling cases.

Findings

The two oscillator models have identical macroscopic properties except for the ORT-induced acceleration.

The acceleration effect caused by the ORT is unique to non-equilibrium systems.

The ORT's impact is isolated by comparing models with and without it.

Abstract

The role of the Onsager reaction term (ORT) is not yet well understood in frustrated coupled oscillator systems, since the Thouless-Anderson-Palmer (TAP) and replica methods cannot be directly applied to these non-equilibrium systems. In this paper, we consider two oscillator associative memory models, one with symmetric and one with asymmetric dilution of coupling. These two systems are ideal for evaluating the effect of the ORT, because, with the exception of the ORT, they have the same order parameter equations. We found that the two systems have identical macroscopic properties, except for the acceleration effect caused by the ORT. This acceleration effect does not exist in any equilibrium system.