The state dependence of integrated, instantaneous, and fluctuating entropy production in quantum and classical processes

Given a fixed physical process, we consider the entropy production (EP) incurred by some initial state $\rho$, additional to the minimal EP incurred by the least-dissipative state $\varphi$. We show that this additional EP has a universal information-theoretic form, given by the contraction of the relative entropy between $\rho$ and $\varphi$ over time. This result holds for total integrated EP, instantaneous EP rate, and fluctuating EP. We derive novel bounds on EP, analyze the thermodynamics of quantum error correction, and propose a thermodynamically-motivated measure of the logical irreversibility of a channel.