scholarly journals Nodal Domain Statistics for Quantum Maps, Percolation, and Stochastic Loewner Evolution

2006 ◽  
Vol 97 (3) ◽  
Author(s):  
J. P. Keating ◽  
J. Marklof ◽  
I. G. Williams
Keyword(s):  
Nodal Domain ◽  
Stochastic Loewner Evolution ◽  
Loewner Evolution

scholarly journals Non-Equilibrium Entropy and Irreversibility in Generalized Stochastic Loewner Evolution from an Information-Theoretic Perspective

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1098
Author(s):  
Yusuke Shibasaki ◽  
Minoru Saito
Keyword(s):  
Second Law Of Thermodynamics ◽  
Time Behavior ◽  
Information Theoretic ◽  
Stochastic Loewner Evolution ◽  
Loewner Evolution ◽  
Long Time ◽  
Jarzynski Equality ◽  
Gibbs Entropy ◽  
Entropic Measure ◽  
Non Equilibrium

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.

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