arXiv subjects

Shin-ichi Sasa

Publications and source records attributed to Shin-ichi Sasa.

At least 91 records · Page 5Linked to original sources

arXiv2014

Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure

We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by the previous measurement as feedback. Consequently, we obtain a set of stationary states corresponding to an exponential family of distributions, each of which shows rare events in the original system as the typical behavior. As a demonstration of our method, we study large deviation statistics of one-dimensional lattice gas models.

cond-mat.stat-mech↗

arXiv2014

Derivation of Hydrodynamics from the Hamiltonian description of particle systems

Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the local Gibbs distribution at initial time. The key concept in the derivation is an identity similar to the fluctuation theorems. The Navier-Stokes equation is obtained as a result of simple perturbation expansions in a small parameter that represents the scale separation.

cond-mat.stat-mech↗

arXiv2014

Calculation of 1RSB transition temperature of spin glass models on regular random graphs under the replica symmetric ansatz

We study $p$-spin glass models on regular random graphs. By analyzing the Franz-Parisi potential with a two-body cavity field approximation under the replica symmetric ansatz, we obtain a good approximation of the 1RSB transition temperature for $p=3$. Our calculation method is much easier than the 1RSB cavity method because the result is obtained by solving self-consistent equations with Newton's method.

cond-mat.stat-mech↗

arXiv2013

Possible extended forms of thermodynamic entropy

Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted, we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy.

cond-mat.stat-mech↗

arXiv2013

Intrinsic Unpredictability of Epidemic Outbreaks on Networks

It has been known that epidemic outbreaks in the SIR model on networks are described by phase transitions. Despite the similarity with percolation transitions, whether an epidemic outbreak occurs or not cannot be predicted with probability one in the thermodynamic limit. We elucidate its mechanism by deriving a simple Langevin equation that captures an essential aspect of the phenomenon. We also calculate the probability of epidemic outbreaks near the transition point.

physics.soc-ph↗

arXiv2013

Work relations for time-dependent states

For time-dependent states generated by an external operation, a generalized free energy may be introduced by the relative entropy with respect to an equilibrium state realized after sufficient relaxation from the time-dependent states. Recently, by studying over-damped systems, Sivak and Crooks presented a formula that relates the generalized free energy with measurable thermodynamic works. We re-derive this relation with emphasizing a connection to an extended Clausius relation proposed in the framework of steady state thermodynamics. As a natural consequence, we generalize this relation to be valid for systems with momentum degrees of freedom, where the Shannon entropy in the generalized free energy is replaced by a symmetric one.

cond-mat.stat-mech↗

arXiv2012

Pure Glass in Finite Dimensions

Pure glass is defined as a thermodynamic phase in which typical equilibrium particle configurations have macroscopic overlaps with one of some special irregular configurations. By employing 128-types of artificial molecules, a pure glass model is constructed in the cubic lattice. It is demonstrated that one-step replica symmetry breaking occurs in the model.

cond-mat.stat-mech↗

arXiv2012

Physics of Large Deviation

A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the fluctuation theorem. Despite such significance, large deviation functions have not been easily obtained in laboratory experiments. Thus, in order to understand the physical significance of large deviation functions, it is necessary to consider their experimental measurability in greater detail. This aspect of large deviation is discussed with the presentation of a future problem.

cond-mat.stat-mech↗

arXiv2011

Thermodynamic formula for the cumulant generating function of time-averaged current

The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under non-equilibrium conditions, we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added, where the modified system is characterized by a variational principle. The formula reminds us of Einstein's fluctuation theory in equilibrium statistical mechanics. Furthermore, since the formula leads to the fluctuation-dissipation relation when the linear response regime is focused on, it is regarded as an extension of the linear response theory to that valid beyond the linear response regime. The formula is also related to previously known theories such as the Donsker-Varadhan theory, the additivity principle, and the least dissipation principle, but it is not derived from them. Examples of its application are presented for a driven Brownian particle on a ring subject to a periodic potential.

cond-mat.stat-mech↗

arXiv2011

Statistical mechanics of glass transition in lattice molecule models

Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An infinite series of irregular ground states are constructed theoretically. By defining a glass order parameter as a collection of the overlap with each ground state, a thermodynamic transition to a glass phase is found in a stratified Wang tiles model on a cubic lattice.

cond-mat.stat-mech↗

arXiv2010

Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems

For Brownian motion of a single particle subject to a tilted periodic potential on a ring, we propose a formula for experimentally determining the cumulant generating function of time-averaged current without measurements of current fluctuations. We first derive this formula phenomenologically on the basis of two key relations: a fluctuation relation associated with Onsager's principle of the least energy dissipation in a sufficiently local region and an additivity relation by which spatially inhomogeneous fluctuations can be properly considered. We then derive the formula without any phenomenological assumptions. We also demonstrate its practical advantage by numerical experiments.

cond-mat.stat-mech↗

arXiv2010

Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States

Among various possible routes to extend entropy and thermodynamics to nonequilibrium steady states (NESS), we take the one which is guided by operational thermodynamics and the Clausius relation. In our previous study, we derived the extended Clausius relation for NESS, where the heat in the original relation is replaced by its "renormalized" counterpart called the excess heat, and the Gibbs-Shannon expression for the entropy by a new symmetrized Gibbs-Shannon-like expression. Here we concentrate on Markov processes describing heat conducting systems, and develop a new method for deriving thermodynamic relations. We first present a new simpler derivation of the extended Clausius relation, and clarify its close relation with the linear response theory. We then derive a new improved extended Clausius relation with a "nonlinear nonequilibrium" contribution which is written as a correlation between work and heat. We argue that the "nonlinear nonequilibrium" contribution is unavoidable, and is determined uniquely once we accept the (very natural) definition of the excess heat. Moreover it turns out that to operationally determine the difference in the nonequilibrium entropy to the second order in the temperature difference, one may only use the previous Clausius relation without a nonlinear term or must use the new relation, depending on the operation (i.e., the path in the parameter space). This peculiar "twist" may be a clue to a better understanding of thermodynamics and statistical mechanics of NESS.

cond-mat.stat-mech↗

arXiv2010

Thermodynamic transition associated with irregularly ordered ground states in a lattice gas model

A two-dimensional lattice gas model is proposed. The ground state of this model with a fixed density is neither periodic nor quasi-periodic. It also depends on system size in an irregular manner. On the other hand, it is ordered in the sense that the entropy density is zero in the thermodynamic limit. The existence of a thermodynamic transition associated with such irregularly ordered ground states is conjectured from a duality relation for a thermodynamic function. This conjecture is supported by a phenomenological argument and numerical experiments.

cond-mat.stat-mech↗

arXiv2010

Shear-induced criticality near a liquid-solid transition of colloidal suspensions

We investigate colloidal suspensions under shear flow through numerical experiments. By measuring the time-correlation function of a bond-orientational order parameter, we find a divergent time scale near a transition point from a disordered fluid phase to an ordered fluid phase, where the order is characterized by a nonzero value of the bond-orientational order parameter. We also present a phase diagram in the $(ρ, \dotγ^{\mathrm{ex}})$ plane, where $ρ$ is the density of the colloidal particles and $\dotγ^{\mathrm{ex}}$ is the shear rate of the solvent. The transition line in the phase diagram terminates at the equilibrium transition point, while a critical region near the transition line vanishes continuously as $\dotγ^{\mathrm{ex}} \rightarrow 0$.

cond-mat.stat-mech↗

arXiv2010

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node bifurcation point in the weak-noise limit, while the final value of the deterministic solution changes discontinuously at the point. A systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method. In this formulation, the critical nature turns out to originate from the neutrality of exiting time from a saddle-point. The theoretical calculation explains results of numerical simulations.

cond-mat.stat-mech↗

arXiv2009

A universal form of slow dynamics in zero-temperature random-field Ising model

The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial condition, we derive exactly an evolution equation for an order parameter. Through a bifurcation analysis of the obtained equation, we reveal a new class of cooperative slow dynamics with the determination of critical exponents.

cond-mat.stat-mech↗

arXiv2009

Two Langevin equations in the Doi-Peliti formalism

A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with a so-called Cole-Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme $X \rightleftarrows X+X$ is investigated as an illustrative example.

cond-mat.stat-mech↗

arXiv2009

Singular perturbation near mode-coupling transition

We study the simplest mode-coupling equation which describes the time correlation function of the spherical p-spin glass model. We formulate a systematic perturbation theory near the mode-coupling transition point by introducing multiple time scales. In this formulation, the invariance with respect to the dilatation of time in a late stage yields an arbitrary constant in a leading order expression of the solution. The value of this constant is determined by a solvability condition associated with a linear singular equation for perturbative corrections in the late stage. The solution thus constructed provides exactly the alpha-relaxation time.

cond-mat.stat-mech↗