both diverge in the limit $T\to0$, even though ${\,\mathrm{d}}S/{\,\mathrm{d}}t$ is well behaved. Equation (\[Pi\_vN\]), in particular, diverges whenever the support of $\rho^*$ is not contained in the support of $\rho$ [@Abe2003; @Audenaert2013]. Such divergence has been the subject of substantial investigation [@Frank2013; @Muller-Lennert2013; @Audenaert2013; @Abe2003; @Esposito2010a; @Pucci2013; @Lendi1988], but whether or not it is a physical consequence of the third law of thermodynamics, or merely a mathematical limitation, remains an open question. This sets an immediate practical limitation since it renders this approach inapplicable to any process whose invariant state is pure, therefore excluding several situations typically encountered in the laboratory. For instance, it excludes the remarkably simple problem of spontaneous emission.

Reference [@Santos2017b] has introduced the idea of using phase-space-entropic measures as an alternative to describe irreversibility in open quantum systems. As was shown, not only does this fix the above mentioned divergences for pure states, but it also allows for a transparent way of extending the framework to nonequilibrium reservoirs. Moreover, it has the advantage of identifying quasiprobability currents in phase space that represent the microscopic manifestations of irreversibility. In Ref. [@Santos2017b], the focus was on Gaussian bosonic states, for which the Wigner function was shown to be 