The Non-equilibrium Behavior of Fluctuation Induced Forces

TL;DR

This paper introduces a general formalism to compute non-equilibrium fluctuation-induced forces, enabling explicit time-dependent calculations and analysis of steady states in systems with dissipative dynamics and colored noise.

Contribution

It provides a novel, unambiguous method to calculate non-equilibrium fluctuation forces using a relation between Laplace transforms and static partition functions.

Findings

First explicit time-dependent non-equilibrium pseudo-Casimir force calculation.

Demonstrates the approach with a sudden temperature change scenario.

Shows how to determine steady-state forces with colored noise.

Abstract

While techniques to compute thermal fluctuation induced, or pseudo-Casimir, forces in equilibrium systems are well established, the same is not true for non-equilibrium cases. We present a general formalism that allows us to unambiguously compute non-equilibrium fluctuation induced forces by specifying the energy of interaction of the fluctuating fields with the boundaries. For a general class of classical fields with dissipative dynamics, we derive a very general relation between the Laplace transform of the time-dependent force and the static partition function for a related problem with a different Hamiltonian. In particular, we demonstrate the power of our approach by computing, for the first time, the explicit time dependence of the non-equilibrium pseudo-Casimir force induced between two parallel plates, upon a sudden change in the temperature of the system. We also show how our results can be used to determine the steady-state behavior of the non-equilibrium force in systems where the fluctuations are driven by colored noise.