Abstract
In this study, we theoretically investigated a generalized stochastic Loewner evolution (SLE) driven by reversible Langevin dynamics in the context of non-equilibrium statistical mechanics. Using the ability of Loewner evolution, which enables encoding of non-equilibrium systems into equilibrium systems, we formulated the encoding mechanism of the SLE by Gibbs entropy-based information-theoretic approaches to discuss its advantages as a means to better describe non-equilibrium systems. After deriving entropy production and flux for the 2D trajectories of the generalized SLE curves, we reformulated the system’s entropic properties in terms of the Kullback–Leibler (KL) divergence. We demonstrate that this operation leads to alternative expressions of the Jarzynski equality and the second law of thermodynamics, which are consistent with the previously suggested theory of information thermodynamics. The irreversibility of the 2D trajectories is similarly discussed by decomposing the entropy into additive and non-additive parts. We numerically verified the non-equilibrium property of our model by simulating the long-time behavior of the entropic measure suggested by our formulation, referred to as the relative Loewner entropy.
Highlights
The irreversibility of non-equilibrium systems has been discussed in numerous fields for decades, the difficulties accompanying their theoretical formulation essentially involve the definition of the concept of entropy [1,2,3]
These formulations assume that time irreversibility in non-equilibrium states is characterized by a non-zero-entropy production rate of the system, and time reversibility holds only when the system is in an equilibrium state with a zero-entropy production rate [7,8,9]
Whereas the information entropy was originally a measure of uncertainty of the events consistently used for describing equilibrium systems, the concept of information is often adopted into the theory of thermodynamics as a quantity we obtain by the measurement of the system [2,21,22]
Summary
The irreversibility of non-equilibrium systems has been discussed in numerous fields for decades, the difficulties accompanying their theoretical formulation essentially involve the definition of the concept of entropy [1,2,3]. Since the pioneering study by Prigogine et al [4], entropy production describing the dissipative open systems far from equilibrium has been studied by employing Gibbs entropy-based approaches [5,6,7,8,9,10,11,12,13,14]. These formulations assume that time irreversibility in non-equilibrium states is characterized by a non-zero-entropy production rate of the system, and time reversibility (or time symmetry) holds only when the system is in an equilibrium state with a zero-entropy production rate [7,8,9]. The recent advance of this perspective has enabled investigation of the generic properties of the entropy production rate [25,26], and the related results were found to be applicable to specific physical problems (e.g., heat conduction [27])
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