Excess heat production, fluctuation-dissipation

GENERALIZATION OF THE FLUCTUATION-DISSIPATION THEOREM FOR EXCESS HEAT PRODUCTION... 

When we consider the dependence of excess heat production on an external transformation, we can connect thermodynamic quantities and underlying dynamics. We have derived the theorem similar to the fluctuation-dissipation theorem [10]. The theorem shows that thermodynamic entropy production such as excess heat can be written as a correlation function between Einstein-Shanon entropy functions. Through the correlation function the thermodynamic entropy production is related to the underlying dynamics. 

In Section II we will review thermodynamics and the fluctuation-dissipation theorem for excess heat production based on the Boltzmann equilibrium distribution. We will also mention the nonequilibrium work relation by Jarzynski. In Section III, we will extend the fluctuation-dissipation theorem for the superstatisitcal equilibrium distribution. The fluctuation-dissipation theorem can be written as a superposition of correlation functions with different temperatures. When the decay constant of a correlation function depends on temperature, we can expect various behaviors in the excess heat. In Section IV, we will consider the case of the microcanonical equilibrium distribution. We will numerically show the breaking of nonergodic adiabatic invariant in the mixed phase space. In the last section, we will conclude and comment. 

This is the reason why we call the theorem the fluctuation-dissipation theorem for excess heat production. 

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