Modelling mechanical equilibration processes of closed quantum systems: a case-study

TL;DR

This paper models the spontaneous thermodynamic processes of a closed quantum system with a moving boundary, capturing the interplay between quantum dynamics and classical boundary motion during compression and expansion.

Contribution

It introduces a coupled differential equation framework that describes quantum and classical boundary dynamics simultaneously, advancing beyond traditional time-dependent Hamiltonian models.

Findings

Successfully models quantum system evolution during thermodynamic transformations.

Captures the mutual influence between quantum states and boundary motion.

Provides insights into non-driven thermodynamic processes in quantum systems.

Abstract

We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating wall, subjected to a constant external pressure. Under the assumption that the wall undergoes classical dynamics, we obtain a system of differential equations that describes the evolution of the quantum system and the motion of the wall. We study the dynamics of such system and the thermodynamics of the process of compression and expansion of the box. Our approach is able to capture several properties of the thermodynamic transformations considered and goes beyond a description in terms of an ad-hoc time-dependent Hamiltonian, considering instead the mutual interactions between the dynamics of the quantum system and the parameters of its Hamiltonian.