Thermodynamics aspects of noise-induced phase synchronization

TL;DR

This paper develops a thermodynamic framework for phase oscillators influenced by multiplicative noise, deriving key thermodynamic quantities and analyzing phase transitions and susceptibility behavior.

Contribution

It introduces a thermodynamic approach to phase oscillators with internal noise, defining a synchronization field and characterizing phase behavior.

Findings

Identification of synchronized and parasynchronized phases

Derivation of free energy, entropy, and specific heat for the system

Observation of susceptibility anomalies similar to complex fluids

Abstract

In this article, we present an approach for the thermodynamics of phase oscillators induced by an internal multiplicative noise. We analytically derive the free energy, entropy, internal energy, and specific heat. In this framework, the formulation of the first law of thermodynamics requires the definition of a synchronization field acting on the phase oscillators. By introducing the synchronization field, we have consistently obtained the susceptibility and analyzed its behavior. This allows us to characterize distinct phases in the system, which we have denoted as synchronized and parasynchronized phases, in analogy with magnetism. The system also shows a rich complex behavior, exhibiting ideal gas characteristics for low temperatures and susceptibility anomalies that are similar to those present in complex fluids such as water.