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Ken Sekimoto

Publications and source records attributed to Ken Sekimoto.

At least 19 recordsLinked to original sources
arXiv2024

Martingale drift of Langevin dynamics and classical canonical spin statistics -- II

In the previous paper we have shown analytically that, if the drift function of the d-dimensional Langevin equation is the Langevin function with a properly chosen scale factor, then the evolution of the drift function is a martingale associated with the histories generated by the very Langevin equation. Moreover, we numerically demonstrated that those generated histories from a common initial data become asymptotically ballistic, whose orientations obey the classical canonical spin statistics under the external field corresponding to the initial data. In the present paper we provide with an analytical explanation of the latter numerical finding by introducing a martingale in the spin functional space. In a specific context the present result elucidates a new physical aspect of martingale theory.

cond-mat.stat-mech↗
arXiv2024

Allosteric propagation of curvature along filament

Can a filament transmit the curvatures across the constituting modules and control them at one of its end? Inspired by the observation of protofilament - constituent biopolymer of microtubule - this question is addressed by a constructive approach. In our model a simple allosteric element in each module couples with the neighboring modules at its interfaces, which gives rise to a single degree of freedom to control the global shape of the filament. The model can be analyzed in analogy with discrete-time dynamical systems having a bifurcation of trans-critical type.

physics.class-ph↗
arXiv2024

Methods and Conversations in (Post)Modern Thermodynamics

Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues.

cond-mat.stat-mech↗
arXiv2023

Martingale drift of Langevin dynamics and classical canonical spin statistics

The martingale characterizes a kind of fairness or unbiased nature of the stochastic process which is associated with another stochastic process. If $x_t$ evolves according to the Langevin equation whose mean drift is $a_t$ as function of $x_t,$ and that $a_t$ as induced stochastic process is martingale in turn associated with the former process, then we show that the amplitude of $a_t$ is the Langevin function, which is originally the canonical response of a single classical Heisenberg spin under static field. Furthermore, the asymptotic limit of $x_t/t$ obeys the ensemble statistics of such Heisenberg spin.

cond-mat.stat-mech↗
arXiv2023

Interplay between Markovianity and Progressive Quenching

Progressive quenching (PQ) is a process in which we sequentially fix a system's degrees of freedom, which would otherwise evolve according to their stochastic dynamics. Previous studies have discovered what we refer to as the hidden martingale property in PQ. Here, we first attribute this martingale property to the canonicity of the two-layer ensemble comprising quenched and thermal ensembles and demonstrate that the Markovian property, coupled with the detailed balance (DB) of the evolution dynamics, underpins this canonicity. We then expand the PQ to the Markovian dynamics on the transition network where the DB is locally upheld. Additionally, we examine the PQ of the systems that evolve through non-Markovian dynamics between consecutive quenching. When non-Markovian dynamics ensure a trajectory-wise DB, such as in an equilibrium spin system with a hidden part, the PQ can occasionally maintain the canonical structure of the overall statistical ensemble, but not always. Lastly, we analytically and numerically investigate the PQ of a non-Markovian spin system with delayed interaction and illustrate how the reduction of spin correlations due to the delay can be compensated by the PQ.

cond-mat.stat-mech↗
arXiv2022

Martingale-induced local invariance in Progressive Quenching

Progressive quenching (PQ) is a stochastic process during which one fixes, one after another, the degrees of freedom of a globally coupled Ising spin system while letting it thermalize through a heat bath. It has previously been shown that during PQ, the mean equilibrium spin value follows a martingale process and this process can characterize the memory of the system. In the present study, we find that the aforementioned martingale implies a local invariance of the path weight for the total quenched magnetization, the Markovian process whose increment is the spin that is fixed last. Consequently, PQ lets the probability distribution for the total quenched magnetization evolve while keeping the Boltzmann-like factor, or a canonical structure, under constraint, which consists of a path-independent potential and a path-counting entropy. Moreover, when the PQ starts from full equilibrium, the probability distribution at each stage of PQ is found to be the limit distribution of what we call recycled quenching, the process in which a randomly chosen quenched spin is unquenched after a single step of PQ. The local invariance is a consequence of the martingale property, and not an application of known theorems for the martingale process.

cond-mat.stat-mech↗
arXiv2020

Memory Through a Hidden Martingale Process in Progressive Quenching

Progressive quenching (PQ) is the stochastic process in which the system's degrees of freedom are sequentially fixed. While such process does not satisfy the local detailed balance, it has been found that the some physical observable of a complete spin network exhibits the martingale property. We studied system's response to the perturbation given at intermediate stages of the PQ. The response at the final stage reveals the persistent memory, and we show that this persistence is a direct consequence of the martingale process behind. Not only the mean response, the shape of the probability distribution at the stage of perturbation is also memorized. Using the hidden martingale process we can predict the final bimodal distribution from the early-stage unimodal distribution in the regime where the unfrozen spins are paramagnetic. We propose a viewpoint that the martingale property is a stochastic conservation law which is supported behind by some stochastic invariance.

cond-mat.stat-mech↗
arXiv2020

Symmetry in Self-Similarity in Space and Time---Short Time Transients and Power-Law Spatial~Asymptote

The self-similarity in space and time (hereafter self-similarity), either deterministic or statistical, is characterized by similarity exponents and a function of scaled variable, called the scaling function. In the present paper, we address mainly the self-similarity in the limit of early stage, as~opposed to the latter one, and also consider the scaling functions that decay or grow algebraically, as~opposed to the rapidly decaying functions such as Gaussian or error function. In particular, in~the case of simple diffusion, our symmetry analysis shows a mathematical mechanism by which the rapidly decaying scaling functions are generated by other polynomial scaling functions. While~the former is adapted to the self-similarity in the late-stage processes, the latter is adapted to the early stages. This paper sheds some light on the internal structure of the family of self-similarities generated by a simple diffusion equation. Then, we present an example of self-similarity for the late stage whose scaling function has power-law tail, and also several cases of self-similarity for the early stages. These examples show the utility of self-similarity to a wider range of phenomena other than the late stage behaviors with rapidly decaying scaling function

math.AP↗
arXiv2018

Progressive quenching - Globally coupled model

We study the processes in which fluctuating elements of a system are progressively fixed (quenched) while keeping the interaction with the remaining unfixed elements. If the interaction is global among the Ising spin elements and if the unfixed part is re-equilibrated each time after fixing an element, the evolution of large system is martingale about the equilibrium spin value of the unfixed spins. Due to this property the system starting from the critical point yields the final magnetization whose distribution shows non-Gaussian and slow transient scaling with the system.

cond-mat.stat-mech↗
arXiv2017

Progressive quenching --- Ising chain models

Of the Ising spin chain with the nearest neighbor or up to the second nearest neighbor interactions, we fixed progressively either a single spin or a pair of neighboring spins at the value they took. Before the subsequent fixation, the unquenched part of the system is equilibrated. We found that, in all four combinations of the cases, the ensemble of quenched spin configurations is the equilibrium ensemble.

cond-mat.stat-mech↗
arXiv2016

Mesoscopic formulas of linear and angular momentum fluxes

Many approaches of coarse-graining have been developed under the names of Cosserat theory or polar-fluid theory, for those materials in which some component elements undergo non-affine deformations, such as elastic materials with inclusions or granular matters. For the complex elements such as living cells, however, the microscopic variables and their dynamics are often unknown, and there have been no systematic theory of coarse-graining from the microscales, nor the formulas like Irving-Kirkwood formula that constitutes the macroscopic stress or couple-stress in terms of some microscale quantities. We show that, for the quasi-steady states, the coarse-graining procedure must generally provides with the Cosserat-type balance equations as long as the procedure keeps track of the conservation of linear and angular momenta, and that the fluxes of these conserved quantities should generally be expressed in the Irving-Kirkwood-type formulas, where the inter- particle distance or forces/torques should be replaced by those associated to the pair of neighboring coarse-graining volumes. This framework, which refers to no particular micro-variables or dynamics, is valid for active complex matters out of equilibrium and with any multi-body interactions.

cond-mat.soft↗
arXiv2014

Non-equilibrium statistical mechanics of the heat bath for two Brownian particles

We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a `system' is both perturbed and sensed by the Brownian particles. Non-local thermal fluctuation give rise to bath-mediated static forces between the particles. Based on the general sum-rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles' dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment as a part of the whole system is important for micron- or nano-scale physics.

cond-mat.stat-mech↗
arXiv2013

From adiabatic piston to non-equilibrium hydrodynamics

Based on the new concept of the {\it momentum transfer deficiency due to dissipation} (MDD), the physical basis of the mechanism of ``adiabatic piston'' is explained. The implication of MDD in terms of hydrodynamics under non-equilibrium steady state also discussed.

cond-mat.stat-mech↗
arXiv2012

A hard disk analysis of momentum deficit due to dissipation

When a Brownian object is in a nonequilibrium steady state, actual force exerted on it is different from one in a thermal equilibrium. In our previous paper [Phys. Rev. Lett. 108 (2012), 160601] we discovered a general principle which relates the missing force to dissipation rates through a concept of momentum deficit due to dissipation (MDD). In this article, we examine the principle using various models based on hard disk gases and Brownian pistons. Explicit expressions of the forces are obtained analytically and the results are compared with molecular dynamics simulations. The good agreement demonstrates the validity of MDD.

cond-mat.stat-mech↗
arXiv2012

Momentum transfer in non-equilibrium steady states

When a Brownian object interacts with non-interacting gas particles under non-equilibrium conditions, the energy dissipation associated to the Brownian motion causes an additional force on the object as a `momentum transfer deficit'. This principle is demonstrated first by a new NESS model and then applied to several known models such as adiabatic piston for which simple explanation has been lacking.

cond-mat.stat-mech↗
arXiv2009

Compatibility between itinerant synaptic receptors and stable postsynaptic structure

The density of synaptic receptors in front of presynaptic release sites is stabilized in the presence of scaffold proteins, but the receptors and scaffold molecules have local exchanges with characteristic times shorter than that of the receptor-scaffold assembly. We propose a mesoscopic model to account for the regulation of the local density of receptors as quasiequilibrium. It is based on two zones (synaptic and extrasynaptic) and multi-layer (membrane, sub-membrane and cytoplasmic) topological organization. The model includes the balance of chemical potentials associated with the receptor and scaffold protein concentrations in the various compartments. The model shows highly cooperative behavior including a "phase change" resulting in the formation of well-defined post-synaptic domains. This study provides theoretical tools to approach the complex issue of synaptic stability at the synapse, where receptors are transiently trapped yet rapidly diffuse laterally on the plasma membrane.

physics.bio-ph↗