Thermodynamics of Maximum Transition Entropy for Quantum Assemblies

TL;DR

This paper introduces a unifying maximum transition entropy framework for quantum non-equilibrium systems, providing a statistical thermodynamics description, analyzing dynamics and stationary states, and exploring implications for wavefunction collapse.

Contribution

It develops a novel maximum transition entropy approach for quantum dynamics, linking non-equilibrium processes with thermodynamic principles and demonstrating its effectiveness through numerical simulations.

Findings

Relaxation rates and stationary states match reference models

Energy exchange and entropy increase during measurement processes

System can absorb heat from superposition states but not from isotropic distributions

Abstract

This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward thermal equilibrium from an arbitrary starting distribution. Using a form based on maximum entropy for this transition distribution leads to a statistical description of open quantum systems with strong parallels to the conventional, maximum-entropy, equilibrium thermostatics. A precise form of the second law of thermodynamics can be stated for this dynamics at every time-point in a trajectory. Numerical results are presented for low-dimensional systems interacting with cavity fields. The dynamics and stationary state are compared to a reference model of a weakly coupled oscillator plus cavity supersystem thermostatted by periodic partial measurements. Despite the absence of an explicit cavity in the present model of open quantum dynamics, both the relaxation rates and stationary state properties closely match the reference. Additionally, the time-course of energy exchange and entropy increase is given throughout an entire measurement process for a single spin system. The results show the process to be capable of initially absorbing heat when starting from a superposition state, but not from an isotropic distribution. Based on these results, it is argued that logical inference in the presence of environmental noise is sufficient to resolve the paradox of wavefunction collapse.