From the adiabatic piston to macroscopic motion induced by fluctuations

TL;DR

This paper demonstrates that in an isolated system with an adiabatic piston, temperature differences can induce systematic macroscopic motion through fluctuation asymmetries, even without macroscopic forces.

Contribution

It provides a rigorous solution showing fluctuation-induced motion in an adiabatic piston system using the Boltzmann equation, revealing a novel fluctuation-driven mechanism.

Findings

Temperature difference causes piston motion toward higher temperature

Fluctuation asymmetry leads to systematic macroscopic movement

Motion occurs despite equal pressures and no macroscopic forces

Abstract

The controversial problem of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated by a piston whose mass is equal to the mass of the fluid particles we obtain a rigorous explicit stationary non-equilibrium solution of the Boltzmann equation. It is shown that at equal pressures on both sides of the piston, the temperature difference induces a non-zero average velocity, oriented toward the region of higher temperature. It thus turns out that despite the absence of macroscopic forces the asymmetry of fluctuations results in a systematic macroscopic motion. This remarkable effect is analogous to the dynamics of stochastic ratchets, where fluctuations conspire with spatial anisotropy to generate direct motion. However, a different mechanism is involved here. The relevance of the discovered motion to the adiabatic piston problem is discussed.