Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process

New exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales are obtained by considering all possible variations of initial conditions of a system, its environment, and correlations between them. First we obtain a new quantum-information theoretic equality for entropy production, valid for an arbitrary initial joint state of system and environment. For any finite-time process with a fixed initial environment, we then show that the contraction of the system's distinction -- relative to the minimally dissipative state -- exactly quantifies its thermodynamic dissipation. The quantum component of this dissipation is the change in coherence relative to the minimally dissipative state. Implications for quantum state preparation and local control are explored. For nonunitary processes -- like the preparation of any particular quantum state -- we find that mismatched expectations lead to divergent dissipation as the actual initial state becomes orthogonal to the anticipated one.
Comment: 6 pages plus 14 pages of appendices, 1 figure