Abstract
We discuss a thermodynamic process with information and justify a general form of fluctuation relation. It shows that the fluctuation relation is valid whatever it is the temperature or Hamiltonian that drives the system out of equilibrium state. Based on the stochastic equation we obtain a nonequilibrium equality that involves both information and time-varying temperature. Through the processing of a harmonic system we demonstrate the validity of the equality by converting information into work. We also discuss the general second law of thermodynamics with time-varying temperature and verify its validity in an example by using information to reduce the total entropy.
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