Nonequilibrium Statistical Physics Research Articles

Spincaloritronic in Magnetic Nanostructures

Using one of the methods of quantum nonequilibrium statistical physics we have investigated the spin transport transverse to the normal metal/ferromagnetic insulator interface in hybrid nanostructures. An approximation of the effective parameters, when each of the interacting subsystems (electron spin, magnon, and phonon) is characterized by its own effective temperature have been considered. We have constructed the macroscopic equations describing the spin-wave current caused by both the resonantly exciting spin subsystem of conduction electrons and an inhomogeneous temperature field in the ferromagnetic insulator. In addition, we have derived the generalized Bloch equations describing the spin-wave current propagation in the insulator and considering the resonant-diffusion nature of the propagation of magnons and their relaxation processes. We have shown that the spin-wave current excitation under combined resonance conditions bears a resonant nature. The formation of the two: injected and thermally excited, different in energies magnon subsystems and the influence of its interaction with phonon drag effect under spin Seebeck effect conditions in the magnetic insulator part of the metal/ferromagnetic insulator/metal structure is studied.

Yet Another Approach to Loschmidt’s Paradox

The works by Lev Petrovich Pitaevskii are reference points for choosing an interesting research topic. An example is the article [Phys. Usp. Vol.54, pp.625-632, 2011] https://doi.org/10.3367/UFNe.0181.201106d.0647 which promotes rigorous results in non-equilibrium statistical physics. In present paper, we rigorously prove that a non-equilibrium state, on the average, is a local entropy minimum. This statement corresponds to the "entropy growth" of statistical mechanics and does not violate time reversal symmetry of microscopic motion: the first-order time derivative of the entropy is zero $\dot{S}=0$, while the second order derivative is non-negative $\ddot{S}\ge 0$.

Semantic information, autonomous agency and non-equilibrium statistical physics.

Shannon information theory provides various measures of so-called syntactic information, which reflect the amount of statistical correlation between systems. By contrast, the concept of 'semantic information' refers to those correlations which carry significance or 'meaning' for a given system. Semantic information plays an important role in many fields, including biology, cognitive science and philosophy, and there has been a long-standing interest in formulating a broadly applicable and formal theory of semantic information. In this paper, we introduce such a theory. We define semantic information as the syntactic information that a physical system has about its environment which is causally necessary for the system to maintain its own existence. 'Causal necessity' is defined in terms of counter-factual interventions which scramble correlations between the system and its environment, while 'maintaining existence' is defined in terms of the system's ability to keep itself in a low entropy state. We also use recent results in non-equilibrium statistical physics to analyse semantic information from a thermodynamic point of view. Our framework is grounded in the intrinsic dynamics of a system coupled to an environment, and is applicable to any physical system, living or otherwise. It leads to formal definitions of several concepts that have been intuitively understood to be related to semantic information, including 'value of information', 'semantic content' and 'agency'.

Application of the fluctuation theorem to motor proteins: from F1-ATPase to axonal cargo transport by kinesin and dynein.

The fluctuation theorem is a representative theorem in non-equilibrium statistical physics actively studied in the 1990s. Relating to entropy production in non-equilibrium states, the theorem has been used to estimate the driving power of motor proteins from fluctuation in their motion. In this review, usage of the fluctuation theorem in experiments on motor proteins is illustrated for biologists, especially those who study mechanobiology, in which force measurement is a central issue. We first introduce the application of the fluctuation theorem in measuring the rotary torque of the rotary motor protein F1-ATPase. Next, as an extension of this application, a recent trial estimating the force generated during cargo transport in vivo by the microtubule motors kinesin and dynein is introduced. Elucidation of the physical mechanism of such transport is important, especially for neurons, in which deficits in cargo transport are deeply related to neuronal diseases. Finally, perspectives on the fluctuation theorem as a new technique in the field of neuroscience are discussed.

Maximum one-shot dissipated work from Rényi divergences.

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.

Nonequilibrium thermodynamics and statistical physics: From rational modeling to its applications

PrefaceThe present volume contains 10 contributed papers presented at the meeting on “Nonequilibrium thermodynamics and statistical physics: From rational modeling to its applications” held during March 16 – 17, 2017 in Hakata, Japan. Each submitted contributed paper was peer-reviewed by at least one referee.The meeting was dedicated to 66th birthday of Prof. Masaru Sugiyama in Nagoya Institute of Technology. The aim of this meeting is to provide the related researchers in the fields of nonequilibrium thermodynamics and statistical physics with an opportunity to get together and to exchange their recent results. Main topics of the meeting are the following:• Rational extended thermodynamics• Nonequilibrium statistical physics• Kinetic theory of rarefied gases• Nonlinear wave propagation• Computational fluid dynamics• Numerical simulation on material scienceValuable discussions from the viewpoints of theoretical physics, chemical physics and applied mathematics were also made after the talks.This international meeting attracted 15 participants from 3 countries, namely, Japan, Italy and China. 12 oral contributions were presented at the meeting.We would like to thank all participants for their essential contributions to the success of the meeting. We are also grateful to the reviewers for their careful reading and prompt response. The meeting was partially supported by JSPS KAKENHI Grant Numbers JP16K17555 (S. T.) JP15K21452 (T.A.) and by National Institute of Technology, Kitakyushu College, Japan.Editors: Shigeru Taniguchi and Takashi Arima

Universality of clone dynamics during tissue development.

The emergence of complex organs is driven by the coordinated proliferation, migration and differentiation of precursor cells. The fate behaviour of these cells is reflected in the time evolution their progeny, termed clones, which serve as a key experimental observable. In adult tissues, where cell dynamics is constrained by the condition of homeostasis, clonal tracing studies based on transgenic animal models have advanced our understanding of cell fate behaviour and its dysregulation in disease (1, 2). But what can be learned from clonal dynamics in development, where the spatial cohesiveness of clones is impaired by tissue deformations during tissue growth? Drawing on the results of clonal tracing studies, we show that, despite the complexity of organ development, clonal dynamics may converge to a critical state characterized by universal scaling behaviour of clone sizes. By mapping clonal dynamics onto a generalization of the classical theory of aerosols, we elucidate the origin and range of scaling behaviours and show how the identification of universal scaling dependences may allow lineage-specific information to be distilled from experiments. Our study shows the emergence of core concepts of statistical physics in an unexpected context, identifying cellular systems as a laboratory to study non-equilibrium statistical physics.

Perspective: Maximum caliber is a general variational principle for dynamical systems.

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Direct verification of the fluctuation-dissipation relation in viscously coupled oscillators.

The fluctuation-dissipation relation, a central result in nonequilibrium statistical physics, relates equilibrium fluctuations in a system to its linear response to external forces. Here we provide a direct experimental verification of this relation for viscously coupled oscillators, as realized by a pair of optically trapped colloidal particles. A theoretical analysis, in which interactions mediated by slow viscous flow are represented by nonlocal friction tensors, matches experimental results and reveals a frequency maximum in the amplitude of the mutual response which is a sensitive function of the trap stiffnesses and the friction tensors. This allows for its location and width to be tuned and suggests the utility of the trap setup for accurate two-point microrheology.

Transitions between superstatistical regimes: Validity, breakdown and applications

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important rôle in analysis of hierarchical complex dynamical systems. Yet, its “canonical” formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show that a multi-scale generalization of the superstatistics paradigm is more versatile, allowing to address such pertinent issues as transmutation of statistics or inter-scale stochastic behavior. To put some flesh on the bare bones, we provide a numerical evidence for a transition between two superstatistics regimes, by analyzing high-frequency (minute-tick) data for share-price returns of seven selected companies. Salient issues, such as breakdown of superstatistics in fractional diffusion processes or connection with Brownian subordination are also briefly discussed.

The exact phase diagram for a class of open multispecies asymmetric exclusion processes

The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric exclusion process with multiple species of particles on a one-dimensional lattice in contact with reservoirs. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram: dynamical expulsion when the density of a species becomes zero throughout the system, and dynamical localisation when the density of a species is nonzero only within an interval far from the boundaries. We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks.

Connecting the dots across time: reconstruction of single-cell signalling trajectories using time-stamped data.

Single-cell responses are shaped by the geometry of signalling kinetic trajectories carved in a multidimensional space spanned by signalling protein abundances. It is, however, challenging to assay a large number (more than 3) of signalling species in live-cell imaging, which makes it difficult to probe single-cell signalling kinetic trajectories in large dimensions. Flow and mass cytometry techniques can measure a large number (4 to more than 40) of signalling species but are unable to track single cells. Thus, cytometry experiments provide detailed time-stamped snapshots of single-cell signalling kinetics. Is it possible to use the time-stamped cytometry data to reconstruct single-cell signalling trajectories? Borrowing concepts of conserved and slow variables from non-equilibrium statistical physics we develop an approach to reconstruct signalling trajectories using snapshot data by creating new variables that remain invariant or vary slowly during the signalling kinetics. We apply this approach to reconstruct trajectories using snapshot data obtained from in silico simulations, live-cell imaging measurements, and, synthetic flow cytometry datasets. The application of invariants and slow variables to reconstruct trajectories provides a radically different way to track objects using snapshot data. The approach is likely to have implications for solving matching problems in a wide range of disciplines.

Collective transport of Lennard–Jones particles through one-dimensional periodic potentials**Project supported by the Natural Science Foundation of Guangdong Province, China (Grant No. 2014A030313367) and the Fundamental Research Fund for the Central Universities, China (Grant No. 11614341).

The surrounding media in which transport occurs contains various kinds of fields, such as particle potentials and external potentials. One of the important questions is how elements work and how position and momentum are redistributed in the diffusion under these conditions. For enriching Fick’s law, ordinary non-equilibrium statistical physics can be used to understand the complex process. This study attempts to discuss particle transport in the one-dimensional channel under external potential fields. Two kinds of potentials—the potential well and barrier—which do not change the potential in total, are built during the diffusion process. There are quite distinct phenomena because of the different one-dimensional periodic potentials. By the combination of a Monte Carlo method and molecular dynamics, we meticulously explore why an external potential field impacts transport by the subsection and statistical method. Besides, one piece of evidence of the Maxwell velocity distribution is confirmed under the assumption of local equilibrium. The simple model is based on the key concept that relates the flux to sectional statistics of position and momentum and could be referenced in similar transport problems.

Active matter

The study of systems with sustained energy uptake and dissipation at the scale of the constituent particles is an area of central interest in nonequilibrium statistical physics. Identifying such systems as a distinct category—Active matter—unifies our understanding of autonomous collective movement in the living world and in some surprising inanimate imitations. In this article I present the active matter framework, briefly recall some early work, review our recent results on single-particle and collective behaviour, including experiments on active granular monolayers, and discuss new directions for the future.

Investigation on the directed transport efficiency of feedback-control ratchet

Brownian motion in the environment of the thermal fluctuations is a long-study issue in nonequilibrium statistical physics. In recent years, the directed transport properties of Brownian ratchets attract the widespread attention of scholars. When a ratchet system possesses the spatio-temporal symmetry-breaking feature, the directed transport can be produced. Although the breakthrough progress in the directed transport of the Brownian ratchet has been made, the energy conversion efficiency of feedback ratchet is not clear. Therefore, the center-of-mass mean velocity and the energy conversion efficiency of coupled ratchet under the influences of the time asymmetry of external force and the spatial asymmetry of external potential are discussed in detail. The overdamped coupled Brownian particles are investigated. Nevertheless, the optimized control of the coupled ratchet is the important for directed transport. Therefore, the closed-loop control which depends on the state of the system is adopted. The dynamic behavior of coupled particles can be described by the overdamped Langevin equation, and the equation is numerically solved by using the stochastic Runge-Kutta algorithm. Some properties of the directed transport can be obtained through this method, such as the center-of-mass mean velocity, the energy conversion efficiency, etc. It is interesting to find that the center-of-mass mean velocity can reach a maximum as the amplitude of external force increases. However, the mean velocity can show the quasi-periodic oscillations with the increase of the period of external force for different values of the spatial asymmetry of external potential. In addition, it can be found that the feedback ratchet needs strong noise to make the directed transport of the ratchet reach the maximum as the coupled strength increases. On the other hand, the energy conversion efficiencies of the feedback ratchet can achieve their corresponding maximum values with the increase of the amplitude of external force for different values of the time asymmetry, and the maximum increases as the time asymmetry increases. However, the efficiency can also show the quasi-periodic oscillations with the increase of the period of the external force for different values of the spatial asymmetry of external potential. Moreover, the energy conversion efficiency can achieve the maximum as the noise strength increases, but the maximum of the efficiency will decrease with the increase of coupling strength. From the discussion above, the optimal values of the time asymmetry, the spatial asymmetry, the period of the external force and the noise strength can promote the directed transport of the feedback coupled Brownian ratchet. These conclusions can provide some guidance in the enhancement of the energy conversion efficiency of a nanomachine.

Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods

Transfer matrices and matrix product operators play a ubiquitous role in the field of many-body physics. This review gives an idiosyncratic overview of applications, exact results, and computational aspects of diagonalizing transfer matrices and matrix product operators. The results in this paper are a mixture of classic results, presented from the point of view of tensor networks, and new results. Topics discussed are exact solutions of transfer matrices in equilibrium and nonequilibrium statistical physics, tensor network states, matrix product operator algebras, and numerical matrix product state methods for finding extremal eigenvectors of matrix product operators.

Deformation of Crystals: Connections with Statistical Physics

We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, as well as a broad introduction to the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, and a variety of depinning transitions are explored. Dislocation dynamics in crystals challenge nonequilibrium statistical physics. Statistical physics provides both cautionary tales of subtle memory effects in nonequilibrium systems and systematic tools designed to address complex scale-invariant behavior on multiple length scales and timescales.

Unreasonable effectiveness of learning neural networks: From accessible states and robust ensembles to basic algorithmic schemes

In artificial neural networks, learning from data is a computationally demanding task in which a large number of connection weights are iteratively tuned through stochastic-gradient-based heuristic processes over a cost function. It is not well understood how learning occurs in these systems, in particular how they avoid getting trapped in configurations with poor computational performance. Here, we study the difficult case of networks with discrete weights, where the optimization landscape is very rough even for simple architectures, and provide theoretical and numerical evidence of the existence of rare-but extremely dense and accessible-regions of configurations in the network weight space. We define a measure, the robust ensemble (RE), which suppresses trapping by isolated configurations and amplifies the role of these dense regions. We analytically compute the RE in some exactly solvable models and also provide a general algorithmic scheme that is straightforward to implement: define a cost function given by a sum of a finite number of replicas of the original cost function, with a constraint centering the replicas around a driving assignment. To illustrate this, we derive several powerful algorithms, ranging from Markov Chains to message passing to gradient descent processes, where the algorithms target the robust dense states, resulting in substantial improvements in performance. The weak dependence on the number of precision bits of the weights leads us to conjecture that very similar reasoning applies to more conventional neural networks. Analogous algorithmic schemes can also be applied to other optimization problems.

Nonequilibrium statistical mechanics of a solid immersed in a continuum

In the introductory part of this survey, we briefly discuss the problems of nonequilibrium statistical physics that arise in the study of energy transport in solids as well as the results available at the moment. In the main part of the survey, we explain, compare, and generalize results obtained in our previous works. We study the dynamics and energy transport in Hamiltonian systems of particles where each particle is weakly perturbed by the interaction with its own stochastic Langevin thermostat. Such systems can be regarded as models of solids that interact weakly with a continuum.

Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle

Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance. It turns out that such an invariance of the Brownian motion is the key to prove the cycle symmetry for diffusion processes on the circle, which says that the distributions of the forming times of the forward and backward cycles, given that the corresponding cycle is formed earlier than the other, are exactly the same. With the aid of the cycle symmetry, we prove the strong law of large numbers, functional central limit theorem, and large deviation principle for the sample circulations and net circulations of diffusion processes on the circle. The cycle symmetry is further applied to obtain various types of fluctuation theorems for the sample circulations, net circulation, and entropy production rate.