Excess thermodynamic functions Fluctuations

The heat capacity peak, characteristic of the transition, reflects the excess heat capacity arising from the enhanced enthalpy fluctuations that occur in the temperature range of the transition. In the case of a two-state transition, the thermodynamic functions are obtained in a straightforward way from the area QD under the peak (corrected for the baseline), which measures the overall enthalpy change resulting from the transition, and the overall heat capacity difference (ACp) ... 

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. 

In Chap. 2 we analyzed single variable linear and non-linear systems with single and multiple stable stationary states by use of the deterministic equations of chemical kinetics. We introduced species-specific affinities and the concept of an excess work with these we showed the existence of a thermodynamic state function 4> and compiled its many interesting properties, see (2.15 2.19), including its relation to fluctuations as given by the stationary solution of the master equation, (2.34). We continue this approach here by turning to systems with more than one intermediate, [1]. 

Liapunov functions) with physical significance, such as the excess work the work and power available from a transient decay to a stationary state macroscopic necessary and sufficient criteria of stability of stationary states thermodynamic criteria for bifurcations from one type of stationary state to another type thermodynamic criteria of relative stability, that is thermodynamic criteria of state selection and a connection of the thermodynamic theory to fluctuations. 

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