Thermodynamic model for feedback control of systems with uncertain macroscopic states

Thermodynamics of feedback control processes, including the minimum work consumption of measurement, work extraction, and erasure processes of thermodynamic small systems have been investigated by researchers. We take systems with uncertain macroscopic states as the study object and study the feedback control processes of nonequilibrium macroscopic systems considering both the information entropy of microscopic states and macroscopic states. First we consider a system set that consists of systems with several macroscopic states and discuss the relations among the average information entropy of the system set, the thermodynamic entropy of the systems and the information entropy of macroscopic states of the systems. Then, we derive the expression of the average maximum net work obtained through feedback control, which relates to the free energy of the systems and the minimum work consumption of the measurement and erasure processes.