Modeling mechanical equilibration processes of closed quantum systems: A case study

We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a nondriven, 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 a 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.