Thermodynamic and Logical Reversibilities Revisited

We review and investigate the general theory of thermodynamics of computation, and derive the fundamental inequalities that set the lower bounds of the work requirement and the heat emission during a computation. These inequalities constitute the generalized Landauer principle, where the information contents are involved in the second law of thermodynamics. We discuss in detail the relationship between the thermodynamic and logical reversibilities; the former is related to the entropy production in the total system including a heat bath, while the latter is related to the entropy change only in the logical states of the memory. In particular, we clarify that any logically irreversible computation can be performed in a thermodynamically reversible manner in the quasi-static limit, which does not contradict the conventional Landauer principle. Our arguments would serve as the theoretical foundation of thermodynamics of computation in terms of modern statistical physics.