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 o ur model by simulating the long-time behavior of the entropic measure suggested by our formulation, referred to as the relative Loewner entropy.

No abstract

Although the fluctuation-dissipation theorem (FDT) is recognized as a general result of statistical physics, its applicability to the non-equilibrium and nonlinear system has not been completely clarified. In this study, we observe that introducing a new type of time coordinate determined by the stochastic Loewner evolution enables the conversion of a certain class of nonlinear Langevin equations into linear ones. The formulation using Loewner time yields a linear response function for the nonlinear systems under a small perturbation. The proposed approach is expected to provide an extension of the conventional FDT in a form applicable to a wide class of non-equilibrium dynamics.

No abstract

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.