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. 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.

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. For the numerically calculated Loewner driving forces, detrended fluctuation analysis was performed, and the morphological characteristics of the neurites were quantified using short-range and long-range scaling exponents. The day in vitro (DIV)-dependent behaviors of the scaling exponents and the associated neurite-type categorizations suggested that differences between healthy and AD neurites can be observed from the early stage (DIV3) of their development. Notably, AD neurites have less long-range autocorrelations than healthy neurites, particularly in the earlier stages (DIV3-10). Immunofluorescence-staining results suggested that these differences precede significant expressions of ß-amyloid and phosphorylated tau, which are known as biological factors causing AD. We expect that these results will lead to a theoretical interpretation of the neurogenerative disease, providing the physical properties of individual neurites with different morphologies.

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 Tc 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. It is notable that while the Loewner driving forces have deterministic properties, they have Gaussian-type probability distributions whose variance increases as T→Tc, indicating that they are examples of the Gaussian chaos. Thus, the obtained Loewner driving forces can be considered a chaotic dynamical system whose bifurcation is dominated by the temperature of the Ising system. This perspective for the dynamical system was discussed in relation to the extension and/or generalization of the stochastic Loewner evolution.