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

2021/05/31 by Michael te Vrugt, Gyula I. Tóth, Raphael Wittkowski +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Dissipative system #Master equation #Phase space #Physics #Quantum #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum process #Spectroscopy and Quantum Chemical Studies #Statistical physics #Wave function #Wave function collapse #cond-mat.stat-mech #math-ph #math.MP #physics.comp-ph #physics.hist-ph #quant-ph

paper · pdf · doi:10.1007/s10825-021-01804-6

published as Journal of Computational Electronics 20, 2209-2231 (2021) · 22 pages, 2 figures

arxiv created 2021/05/31 · openalex publication_date 2021/05/31 · openalex created_date 2021/11/22 · arxiv updated 2021/12/21 · openalex updated_date 2026/08/05

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.

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