  It is a central question in quantum thermodynamics to determine how
irreversible is a process that transforms an initial state $\rho$ to a final
state $\sigma$, and whether such irreversibility can be thought of as a useful
resource. For example, we might ask how much work can be obtained by
thermalizing $\rho$ to a thermal state $\sigma$ at temperature $T$ of an
ambient heat bath. Here, we show that, for different sets of resource-theoretic
thermodynamic operations, the amount of entropy produced along a transition is
characterized by how reversible the process is. More specifically, this entropy
production depends on how well we can return the state $\sigma$ to its original
form $\rho$ without investing any work. At the same time, the entropy
production can be linked to the work that can be extracted along a given
transition, and we explore the consequences that this fact has for our results.
We also exhibit an explicit reversal operation in terms of the Petz recovery
channel coming from quantum information theory. Our result establishes a
quantitative link between the reversibility of thermodynamical processes and
the corresponding work gain.
