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

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.

Quantifying scaling exponents for neurite morphology of in vitro-cultured human iPSC-derived neurons using discrete Loewner evolution: A statistical-physical approach to the neuropathology in Alzheimer's disease.

Defining the morphological disorders causing neurodegenerative diseases is an unresolved problem. In this study, we propose a statistical-physical approach to quantify neurite morphology and evaluate the pathological states induced by Alzheimer's disease (AD). We analyzed the two-dimensional morphologies of neurites of in vitro-cultured human induced-pluripotent stem cell-derived neurons, reprogrammed from both a healthy person and a patient with AD, using discrete chordal Loewner evolution.

Loewner driving force of the interface in the 2-dimensional Ising system as a chaotic dynamical system.

The interfaces in the 2-dimensional (2D) ferromagnetic Ising system below and at the critical temperature T were numerically analyzed in the framework of discrete Loewner evolution. We numerically calculated Loewner driving forces corresponding to the interfaces in the 2D Ising system and analyzed them using nonlinear time series analyses. We found that the dynamics of the Loewner driving forces showed chaotic properties wherein their intermittency, sensitivity to initial condition, and autocorrelation change depending on the temperature T of the system.