The Second Law of Controlled Linear Stochastic Thermodynamic Systems over a Noiseless Digital Channel

摘要

It is known that the conventional second law of thermodynamics is not applicable to thermodynamic systems when feedback control is applied to such systems. A generalized form of the second law should be introduced in this case, which contains an additive term that describes the correlation between the microstates and the measurement outcomes. In this study, we consider a situation where a linear stochastic thermodynamic system, which is in contact with a heat bath, is controlled over a noiseless digital channel to evaluate how channel capacity and control performance are interrelated considering the second law of thermodynamics. We show that in this case, the second law of thermodynamics is inclusive of a term that represents channel capacity. We then show that given a fixed value of free energy difference, we can extract a larger amount of work from the system and obtain higher control performance if more channel capacity is used, in the case where an optimal controller and a proper encoder are used in the control system.