The controversial piston in the thermodynamic limit

TL;DR

This paper investigates the behavior of an adiabatic piston system in the thermodynamic limit, showing that piston motion becomes deterministic and analyzing the approach to equilibrium through simulations and comparisons with finite systems.

Contribution

It introduces a new analysis of the adiabatic piston in the thermodynamic limit, demonstrating deterministic piston motion and equilibrium behavior under specific scaling assumptions.

Findings

Piston motion becomes deterministic in the thermodynamic limit.

The approach to equilibrium is characterized under simplifying assumptions.

Numerical simulations illustrate the theoretical results.

Abstract

We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided in two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area $A$ of the container, the number $N$ of particles, and the mass $M$ of the piston go to infinity keeping $\frac{A}M $ and $\frac{N}M $ fixed. We show that in this limit the motion of the piston is deterministic. Introducing simplifying assumptions we discuss the approach to equilibrium and we illustrate the results with numerical simulations. The comparison with the case of a system with finite $(A, N, M)$ will be presented. We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided in two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area $A$ of the container, the number $N$ of particles, and the mass $M$ of the piston go to infinity keeping $\frac{A}M $ and $\frac{N}M $ fixed. We show that in this limit the motion of the piston is deterministic. Introducing simplifying assumptions we discuss the approach to equilibrium and we illustrate the results with numerical simulations. The comparison with the case of a system with finite $(A, N, M)$ will be presented.