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

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.

arXiv comment10 pages, 11 figures

References in corpus (15)

• A nonequilibrium equality for free energy differences
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• The Role of Relative Entropy in Quantum Information Theory
• Quantum Thermodynamics
• Fluctuation theorems: Work is not an observable
• Maximal work extraction from quantum systems
• Irreversible entropy production, from quantum to classical
• More bang for your buck: Towards super-adiabatic quantum engines
• Generalized Clausius inequality for nonequilibrium quantum processes
• Understanding quantum measurement from the solution of dynamical models
• Quantum engine efficiency bound beyond the second law of thermodynamics
• Nonequilibrium entropy production for open quantum systems
• Quantum thermal absorption machines: refrigerators, engines and clocks
• Ultra-cold Single-Atom Quantum Heat Engines
• A quantum particle in a box with moving walls