Recent Publications

The mean first passage time is the average amount of time it takes for a random walker departing from a source location to reach a target location for the first time.

It has been known that the mean first passage time of random walks on a random fractal has been known obeys a power law scaling with the distance between a source and a target site with a universal exponent.

We found that the scaling exponent highly depends on the location of the source and target, even when the degree distribution of the medium is homogenous as in a two-dimensional critical percolation cluster.

The role of the location of a site in the first passage process is encoded in the heterogeneous distribution of the random walk centrality, a measure of accessibility to a site.

We show that the mean first passage time is determined by competition between direct paths and indirect paths detouring via the domain characterized by high random walk centralities.

As a consequence of the competition, the mean first passage time displays a crossover scaling between a short-distance regime, where direct paths are dominant, and a long-distance regime, where indirect paths are dominant. 

The fluctuation-response relation of chemical reaction networks driven far from equilibrium has been explored.

A specific perturbation was chosen, involving logarithmic changes in the reaction rates of chemical reactions, and the response of the mean number of a chemical species was observed.

In the case of uni-directional perturbations, where either one of the reaction rates in a reaction channel is perturbed, the maximum response is bounded by number fluctuations.

In the case of bi-directional perturbations, where both reaction rates in a reaction channel are perturbed, the maximum response is further bounded by a function of the maximum thermodynamic driving force, in addition to number fluctuations.

These trade-offs between response, fluctuation, and thermodynamic driving force have been proven for linear chemical reaction networks and a class of nonlinear chemical reaction networks involving a single chemical species

Furthermore, numerical results for several model systems suggest that the trade-offs persist across a broad class of chemical reaction networks.

The fluctuation-dissipation theorem (FDT) characterizes the response of equilibrium systems to perturbations in terms of experimentally-measurable equilibrium correlation functions.

However, far from equilibrium, the FDT loses its simplicity, and disparate analysis methods emerge.

One approach has been to re-establish the connection between response and correlation functions around nonequilibrium steady states, and a complementary approach has been to characterize violations of the equilibrium FDT.

In the tradition of studying violations of the FDT, we demonstrate for one-dimensional diffusions that the response can be constrained by the nonequilibrium driving.

We unravel an arbitrary perturbation of a diffusive steady state into a linear combination of three classes of perturbations that can be individually analyzed.

For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.

Linearized hydrodynamic transport equations have succeeded in describing how spatial inhomogeneities in macroscopic systems relax, in and out of equilibrium.

The speed of the relaxation is determined by the transport coefficients, for which statistical mechanics offers microscopic expressions near equilibrium, known as Green-Kubo relations.

To extend the same idea to far-from-equilibrium, we find a class of perturbations whose response is linked to nonequilibrium steady-state correlation functions. 

As a consequence, we derive nonequilibrium Green-Kubo relations for the transport coefficients of two types of hydrodynamic variables: local densities of conserved quantities and broken-symmetry modes.

Our predictions are analytically and numerically demonstrated for two model systems: particle density diffusion in a fluid of active Brownian particles and phase diffusion in the noisy Kuramoto model on a square lattice.

The thermodynamics uncertainty relation has provided the entropy production as a lower bound for the uncertainty of a current of a system in the nonequilibrium steady state.

Though a few bound on the uncertainty have been derived for underdamped Langevin systems, their physical meanings are not transparent, and more importantly, they do not converge to the proven thermodynamic uncertainty relation in the overdamped limit. 

We showed that the original thermodynamic uncertainty relation is inevitably violated for finite times underdamped Langevin systems due to its innate ballistic short-time behavior.

Supported by numerical evidence, we conjectured that the uncertainty of currents is bound from below by that obtained from a corresponding free diffusion process.

This bound converges to the original thermodynamic uncertainty relation in the overdamped limit. 

We also numerically studied the possibility of the applicability of the conjectured bound to higher spacial dimensional systems.