Non-stationary solutions driven by thermodynamic power in the white-noise Langevin model

TL;DR

This paper derives the average thermodynamic power in a time-dependent Langevin model, showing how it influences whether the system reaches a stationary or non-stationary state, with explicit models illustrating different dynamics.

Contribution

It introduces a Green's function approach to derive thermodynamic power and analyzes its role in system dynamics under various external potential protocols.

Findings

Power determines stationarity of solutions

Explicit models demonstrate different dynamic behaviors

Method applicable to various time-dependent potentials

Abstract

The average thermodynamic power of a time-dependent external potential in the white-noise Langevin model is derived using a Green's function solution. The power appears as a driving term in the differential equation for the average energy and determines whether the solution is stationary or non-stationary. Different dynamics are illustrated with explicit models: a linear potential with a static magnetic field, a linear potential perturbed with an oscillating component and a magnetic field switch modeled using a $\tanh$ protocol.