arXiv subjects

Soya Shinkai

Publications and source records attributed to Soya Shinkai.

7 recordsLinked to original sources

arXiv2026

Exact Generalized Langevin Dynamics of Pair Coordinates in Elastic Networks

Generalized Langevin equations (GLEs) provide a powerful framework for describing slow dynamics in soft-matter systems, but deriving an exact homogeneous GLE (hGLE) for a reaction coordinate from an underlying many-body system remains generally difficult. Here, we analytically derive an exact hGLE for the relative coordinate of two tagged beads in arbitrary elastic networks. The memory kernel and effective restoring force are expressed explicitly in terms of the network matrices, thereby providing a systematic reduction of the high-dimensional network dynamics to a pair coordinate. Within the small-displacement approximation, we further derive a hGLE for the inter-bead distance, a central observable in distance-sensitive single-molecule experiments. These results therefore have broad potential applications in modeling proteins and other soft-matter systems.

cond-mat.soft↗

arXiv2024

Generalized Langevin dynamics for single beads in linear elastic network

We derive generalized Langevin equations (GLEs) for single beads in linear elastic networks. In particular, the derivations of the GLEs are conducted without employing normal modes, resulting in two distinct representations in terms of resistance and mobility kernels. The fluctuation-dissipation relations are also confirmed for both GLEs. Subsequently, we demonstrate that these two representations are interconnected via Laplace transforms. Furthermore, another GLE is derived by utilizing a projection operator method, and it is shown that the equation obtained through the projection scheme is consistent with the GLE with the resistance kernel. As simple examples, the general theory is applied to the Rouse model and the ring polymer, where the GLEs with the resistance and mobility kernels are explicitly derived for arbitrary positions of the tagged bead in these models. Finally, the GLE with the mobility kernel is also derived for the elastic network with hydrodynamic interactions under the pre-averaging approximation.

cond-mat.soft↗

arXiv2014

Generalized Lyapunov exponent as a unified characterization of dynamical instabilities

The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov exponent, as a unified characterization of non-exponential and exponential dynamical instabilities in one-dimensional maps. Chaos is classified into three different types, i.e., super-exponential, exponential, and sub-exponential dynamical instabilities. Using one-dimensional maps, we demonstrate super-exponential and sub-exponential chaos and quantify the dynamical instabilities by the Lyapunov pair. In sub-exponential chaos, we show super-weak chaos, which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth. The scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process, which is related to infinite ergodic theory.

nlin.CD↗

arXiv2014

Dissipative Heat Decomposition in Stochastic Energetics: Implication of the Instantaneous Diffusion Coefficient in Nonequilibrium Steady States

We give a decomposition expression for dissipative heat using the instantaneous diffusion coefficient in a nonequilibrium steady state. The dissipative heat can be expressed using three diffusion coefficients: instantaneous, equilibrium, and drift. An experimental application of the decomposition expression permits us to evaluate the heat dissipation rate from single-trajectory data only. We also numerically demonstrate this method.

cond-mat.stat-mech↗

arXiv2014

Distributional behavior of time averages of non-$L^1$ observables in one-dimensional intermittent maps with infinite invariant measures

In infinite ergodic theory, two distributional limit theorems are well-known. One is characterized by the Mittag-Leffler distribution for time averages of $L^1(m)$ functions, i.e., integrable functions with respect to an infinite invariant measure. The other is characterized by the generalized arc-sine distribution for time averages of non-$L^1(m)$ functions. Here, we provide another distributional behavior of time averages of non-$L^1(m)$ functions in one-dimensional intermittent maps where each has an indifferent fixed point and an infinite invariant measure. Observation functions considered here are non-$L^1(m)$ functions which vanish at the indifferent fixed point. We call this class of observation functions weak non-$L^1(m)$ function. Our main result represents a first step toward a third distributional limit theorem, i.e., a distributional limit theorem for this class of observables, in infinite ergodic theory. To prove our proposition, we propose a stochastic process induced by a renewal process to mimic a Birkoff sum of a weak non-$L^1(m)$ function in the one-dimensional intermittent maps.

nlin.CD↗

arXiv2014

$1/f$ Spectrum and 1-Stable Law in One-Dimensional Intermittent Map with Uniform Invariant Measure and Nekhoroshev Stability

We investigate ergodic properties of a one-dimensional intermittent map that has not only an indifferent fixed point but also a singular structure such that a uniform measure is invariant under mapping. The most striking aspect of our model is that stagnant motion around the indifferent fixed point is induced by the log-Weibull law, which is derived from Nekhoroshev stability in the context of nearly-integrable Hamiltonian systems. Using renewal analysis, we derive a logarithmic inverse power decay of the correlation function and a $1/ω$-like power spectral density. We also derive the so-called 1-stable law as a component of the time-average distribution of a simple observable function. This distributional law enables us to calculate a logarithmic inverse power law of large deviations. Numerical results confirm these analytical results. Finally, we discuss the relationship between the parameters of our model and the degrees of freedom in nearly-integrable Hamiltonian systems.

nlin.CD↗

arXiv2014

Energetics of single active diffusion trajectories

The fundamental insight into Brownian motion by Einstein is that all substances exhibit continual fluctuations due to thermal agitation balancing with the frictional resistance. However, even at thermal equilibrium, biological activity can give rise to non-equilibrium fluctuations that cause ``active diffusion" in living cells. Because of the non-stationary and non-equilibrium nature of such fluctuations, mean square displacement analysis, relevant only to a steady state ensemble, may not be the most suitable choice as it depends on the choice of the ensemble; hence, a new analytical method for describing active diffusion is desired. Here we discuss the stochastic energetics of a thermally fluctuating single active diffusion trajectory driven by non-thermal random forces. Heat dissipation, usually difficult to measure, can be estimated from the active diffusion trajectory; guidelines on the analysis such as criteria for the time resolution and driving force intensity are shown by a statistical test. This leads to the concept of an ``instantaneous diffusion coefficient" connected to heat dissipation that may be used to analyse the activity and molecular transport mechanisms of living systems.

cond-mat.soft↗