  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.
