  Quantifying the degree of irreversibility of an open system dynamics
represents a problem of both fundamental and applied relevance. Even though a
well-known framework exists for thermal baths, the results give diverging
results in the limit of zero temperature and are also not readily extended to
nonequilibrium reservoirs, such as dephasing baths. Aimed at filling this gap,
in this paper we introduce a phase-space-entropy production framework for
quantifying the irreversibility of spin systems undergoing Lindblad dynamics.
The theory is based on the spin Husimi-Q function and its corresponding
phase-space entropy, known as Wehrl entropy. Unlike the von Neumann entropy
production rate, we show that in our framework, the Wehrl entropy roduction
rate remains valid at any temperature and is also readily extended to arbitrary
nonequilibrium baths. As an application, we discuss the irreversibility
associated with the interaction of a two-level system with a single-photon
pulse, a problem which cannot be treated using the conventional approach.
