Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

TL;DR

This paper derives phase-space equations for key spontaneous collapse models in quantum mechanics and tests their role in thermodynamic irreversibility, finding that GRW-type perturbations do not induce thermodynamic behavior.

Contribution

It provides the first derivation of Wigner function master equations for major collapse models and tests their impact on thermodynamic irreversibility through simulations.

Findings

GRW models' stochasticity does not produce thermodynamic irreversibility.

Simulations show GRW perturbations do not lead to classical thermodynamic behavior.

The proposed GRW-based mechanism for equilibration is not supported.

Abstract

Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models - Ghirardi-Rimini-Weber (GRW) theory, continuous spontaneous localization (CSL) model, Di\'osi-Penrose model, and dissipative GRW model - in the Wigner framework. The resulting master equations are approximated by Fokker-Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert's suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed.