  The generalized stochastic Loewner evolution (SLE) driven by reversible
Langevin dynamics was theoretically investigated in the context of
non-equilibrium statistical mechanics. The recent study of the authors revealed
that the Loewner evolution enables encoding the non-equilibrium (irreversible)
processes into equilibrium (reversible) processes. In this study, by Gibbs
entropy-based information-theoretic approaches, we formulated this encoding
mechanism of the SLE to discuss its advantages as a mean to better describe
non-equilibrium states. After deriving entropy production and flux for the 2D
trajectories of the generalized SLE curve, 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 trajectory was likewise discussed by decomposing its
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.
