The partition function in the quantum-to-classical transition

Abstract

In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of positions and momenta, along with the probability distribution that accounts for the inherent uncertainty in measuring particle locations. Within this framework, the quantum-to-classical transition arises naturally, maintaining consistency between dynamics and statistical mechanics.