Thermodynamic Lower Bounds of Deviation from Instantaneous Canonical State

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We address the issue of the characterization of the nonequilibrium states for the time-dependent processes of a system interacting with a large reservoir, which is initially prepared in an equilibrium state. During the time evolution, we apply an external force to the system so that the actual density matrix is quantitatively different from the canonical state specified by the time-dependent system Hamiltonian. To express how the external forcing causes the deviation from equilibrium, we give a class of thermodynamic expressions for the lower bounds of the distance between the actual nonequilibrium state and the corresponding canonical state. The lower bounds are thermodynamically expressed only in terms of the strength of the forcing and its consequent entropy production rate.

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