Nonequilibrium Statistical Physics Research Articles

Simple and efficient methods for local structural analysis in polydisperse hard disk systems.

In nonequilibrium statistical physics, quantifying the nearest (and higher-order) neighbors and free volumes of particles in many-body systems is crucial to elucidating the origin of macroscopic collective phenomena, such as glass/granular jamming transitions and various aspects of the behavior of active matter. However, conventional techniques (based on a fixed-distance cutoff or the Voronoi construction) have mainly been applied to equilibrated, homogeneous, and monodisperse particle systems. In this paper, we implement simple and efficient methods for local structure analysis in nonequilibrium, inhomogeneous, and polydisperse hard disk systems. We show how these novel methods can overcome the difficulties encountered by conventional techniques as well as demonstrate some applications.

Short-range correlation of stress chains near solid-to-liquid transition in active monolayers.

Using a three-dimensional model of cell monolayers, we study the spatial organization of active stress chains as the monolayer transitions from a solid to a liquid state. The critical exponents that characterize this transition map the isotropic stress percolation onto the two-dimensional random percolation universality class, suggesting short-range stress correlations near this transition. This mapping is achieved via two distinct, independent pathways: (i) cell-cell adhesion and (ii) active traction forces. We unify our findings by linking the nature of this transition to high-stress fluctuations, distinctly linked to each pathway. The results elevate the importance of the transmission of mechanical information in dense active matter and provide a new context for understanding the non-equilibrium statistical physics of phase transition in active systems.

Fluctuation Relation for the Dissipative Flux: The Role of Dynamics, Correlations and Heat Baths.

The fluctuation relation stands as a fundamental result in nonequilibrium statistical physics. Its derivation, particularly in the stationary state, places stringent conditions on the physical systems of interest. On the other hand, numerical analyses usually do not directly reveal any specific connection with such physical properties. This study proposes an investigation of such a connection with the fundamental ingredients of the derivation of the fluctuation relation for the dissipation, which includes the decay of correlations, in the case of heat transport in one-dimensional systems. The role of the heat baths in connection with the system's inherent properties is then highlighted. A crucial discovery of our research is that different lattice models obeying the steady-state fluctuation relation may do so through fundamentally different mechanisms, characterizing their intrinsic nature. Systems with normal heat conduction, such as the lattice ϕ4 model, comply with the theorem after surpassing a certain observational time window, irrespective of lattice size. In contrast, systems characterized by anomalous heat conduction, such as Fermi-Pasta-Ulam-Tsingou-β and harmonic oscillator chains, require extended observation periods for theoretical alignment, particularly as the lattice size increases. In these systems, the heat bath's fluctuations significantly influence the entire lattice, linking the system's fluctuations with those of the bath. Here, the current autocorrelation function allows us to discern the varying conditions under which different systems satisfy with the fluctuation relation. Our findings significantly expand the understanding of the stationary fluctuation relation and its broader implications in the field of nonequilibrium phenomena.

Solution of the discrete Boltzmann equation: based on the finite volume method

Mesoscopic methods serve as a pivotal link between the macroscopic and microscopic scales, offering a potent solution to the challenge of balancing physical accuracy with computational efficiency. Over the past decade, significant progress has been made in the application of the discrete Boltzmann method (DBM), which is a mesoscopic method based on a fundamental equation of nonequilibrium statistical physics (i.e., the Boltzmann equations), in the field of nonequilibrium fluid systems. The DBM has gradually become an important tool for describing and predicting the behavior of complex fluid systems. The governing equations comprise a set of straightforward and unified discrete Boltzmann equations, and the choice of their discrete format significantly influences the computational accuracy and stability of numerical simulations. In a bid to bolster the reliability of these simulations, this paper utilizes the finite volume method as a solution for handling the discrete Boltzmann equations. The finite volume method stands out as a widely employed numerical computation technique, known for its robust conservation properties and high level of accuracy. It excels notably in tackling numerical computations associated with high-speed compressible fluids. For the finite volume method, the value of each control volume corresponds to a specific physical quantity, which makes the physical connotation clear and the derivation process intuitive. Moreover, through the adoption of suitable numerical formats, the finite volume method can effectively minimize numerical oscillations and exhibit strong numerical stability, thus ensuring the reliability of computational results. Particularly, the MUSCL format where a flux limiter is introduced to improve the numerical robustness is adopted for the reconstruction in this paper. Ultimately, the DBM utilizing the finite volume method is rigorously validated to assess its proficiency in addressing flow issues characterized by pronounced discontinuities. The numerical experiments encompass scenarios involving shock waves, Lax shock tubes, and acoustic waves. The results demonstrate the method's precise depiction of shock wave evolution, rarefaction waves, acoustic phenomena, and material interfaces. Furthermore, it ensures the conservation of mass, momentum, and energy within the system, as well as accurately measures the hydrodynamic and thermodynamic nonequilibrium effects of the fluid system. Compared with the finite difference method, the finite volume method is also more convenient and flexible in dealing with boundary conditions of different geometries, and can be adapted to a variety of systems with complex boundary conditions. Consequently, the finite volume method further broadens the scope of DBM in practical applications.

Computational phase transition signature in Gibbs sampling

Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors—be it quantum or stochastic annealing devices—which embed problem instances and evolve a physical system into a low-energy ensemble to recover a probability distribution. At a critical constraint to variable ratio, satisfiability (SAT) problem instances exhibit a SAT-UNSAT transition (frustrated to frustration free). Algorithms require increasing computational resources from this critical point. This is a so called, algorithmic or computational phase transition and has extensively been studied. In this paper we consider the complexity in sampling and recovering ground states from resultant distributions of a physics based processor. In particular, we first consider the ideal Gibbs distributions at some fixed inverse temperature and observe that the success probability in sampling and recovering ground states decrease for instances starting at the critical density. Furthermore, simulating the Gibbs distribution, we employ Ising spin dynamics, which play a crucial role in understanding of non-equilibrium statistical physics, to find their steady states of 2-SAT Hamiltonians. We observe that beyond the critical density, the probability of sampling ground states decreases. Our results apply to several contemporary devices and provide a means to experimentally probe a signature of the computational phase transition.

Stationarity of quantum statistical ensembles at first-order phase transition points

We study the dynamics of quantum statistical ensembles at first-order phase transition points of finite macroscopic systems. First, we show that at the first-order phase transition point of the system, with an order parameter that does not commute with the Hamiltonian, any quantum state with an order parameter that has a nonzero value always evolves towards a macroscopically distinct state after a sufficiently long time. From this result, we argue that the stationarity required for statistical ensembles should be interpreted as stationarity on a sufficiently long but finite timescale. Finally, we prove that the density matrix of the squeezed ensemble, a class of generalized statistical ensembles proposed as the only concrete method of constructing phase coexistence states applicable to general quantum systems, is locally stationary on timescales diverging in the thermodynamic limit. Our results support the validity of the squeezed ensemble from a dynamical point of view and open the door to nonequilibrium statistical physics at the first-order phase transition point.

The influences of acceleration on compressible Rayleigh–Taylor instability with non-equilibrium effects

Rayleigh–Taylor (RT) instability is a classical interface instability of great importance in nature and engineering fields. In this paper, the influences of acceleration on the compressible RT instability is investigated by using the discrete Boltzmann method based on non-equilibrium statistical physics. The differences in RT systems with various accelerations have been analyzed through the physical gradients and non-equilibrium measures. It is interesting to find that the global temperature gradient, the maximum Mach number, and the non-equilibrium strength increase initially, reduce afterwards, and have peaks in the dynamic process. Specifically, in the early stage, the global temperature gradient of the fluid system is higher for a case with larger acceleration, and there is an exponential relationship between them. Moreover, the maximum Mach number is located at the heavy fluid that drops fast in the system’s midsection, rises more sharply, and reaches the peak earlier for a larger acceleration. In addition, for a larger acceleration, the non-equilibrium strength rises (reduces) faster in the early (later) stage, and presents an exponential relationship between them in the early stage as well. From the kinetic perspective, these results further enrich our understanding of the physical mechanism of the compressible RT instability with both hydrodynamic and thermodynamic non-equilibrium effects.

The entropy production of stationary diffusions

The entropy production rate is a central quantity in non-equilibrium statistical physics, scoring how far a stochastic process is from being time-reversible. In this paper, we compute the entropy production of diffusion processes at non-equilibrium steady-state under the condition that the time-reversal of the diffusion remains a diffusion. We start by characterising the entropy production of both discrete and continuous-time Markov processes. We investigate the time-reversal of time-homogeneous stationary diffusions and recall the most general conditions for the reversibility of the diffusion property, which includes hypoelliptic and degenerate diffusions, and locally Lipschitz vector fields. We decompose the drift into its time-reversible and irreversible parts, or equivalently, the generator into symmetric and antisymmetric operators. We show the equivalence with a decomposition of the backward Kolmogorov equation considered in hypocoercivity theory, and a decomposition of the Fokker-Planck equation in GENERIC form. The main result shows that when the time-irreversible part of the drift is in the range of the volatility matrix (almost everywhere) the forward and time-reversed path space measures of the process are mutually equivalent, and evaluates the entropy production. When this does not hold, the measures are mutually singular and the entropy production is infinite. We verify these results using exact numerical simulations of linear diffusions. We illustrate the discrepancy between the entropy production of non-linear diffusions and their numerical simulations in several examples and illustrate how the entropy production can be used for accurate numerical simulation. Finally, we discuss the relationship between time-irreversibility and sampling efficiency, and how we can modify the definition of entropy production to score how far a process is from being generalised reversible.

Bayesian inference of polymerase dynamics over the exclusion process.

Transcription is a complex phenomenon that permits the conversion of genetic information into phenotype by means of an enzyme called RNA polymerase, which erratically moves along and scans the DNA template. We perform Bayesian inference over a paradigmatic mechanistic model of non-equilibrium statistical physics, i.e. the asymmetric exclusion processes in the hydrodynamic limit, assuming a Gaussian process prior for the polymerase progression rate as a latent variable. Our framework allows us to infer the speed of polymerases during transcription given their spatial distribution, while avoiding the explicit inversion of the system's dynamics. The results, which show processing rates strongly varying with genomic position and minor role of traffic-like congestion, may have strong implications for the understanding of gene expression.

Quantum Mechanics and Quantum Field Theory: Algebraic and Geometric Approaches

This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory, including recent results. It is based on the algebraic approach in which the starting point is a star-algebra and on the geometric approach in which the starting point is a convex set of states. Standard formulas for quantum probabilities are derived from decoherence. This derivation allows us to go beyond quantum theory in the geometric approach. Particles are defined as elementary excitations of the ground state (and quasiparticles as elementary excitations of any translation invariant state). The conventional scattering matrix does not work for quasiparticles (or even for particles if the theory does not have particle interpretation). The analysis of scattering in these cases is based on the notion of an inclusive scattering matrix, which is closely related to inclusive cross-sections. It is proven that the conventional scattering matrix can be expressed in terms of Green functions (LSZ formula) and the inclusive scattering matrix can be expressed in terms of generalized Green functions that appear in the Keldysh formalism of non-equilibrium statistical physics. The derivation of the expression of the evolution operator and other physical quantities in terms of functional integrals is based on the notion of the symbol of an operator; these arguments can be applied in the geometric approach as well. In particular, this result can be used to provide a simple derivation of the diagram technique for generalized Green functions. The notion of an inclusive scattering matrix makes sense in the geometric approach, although it seems that a definition of the conventional scattering matrix cannot be provided in this situation. The geometric approach is used to show that quantum mechanics and its generalizations can be considered as classical theories where our devices are able to measure only a part of the observables.

Arbitrage Equilibrium, Invariance, and the Emergence of Spontaneous Order in the Dynamics of Bird-like Agents.

The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these approaches do not seem to recognize explicitly their critical feature: namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. Here, we propose a game-theoretic framework, statistical teleodynamics, that demonstrates that the bird-like agents self-organize dynamically into flocks to approach a stable arbitrage equilibriumof equal effective utilities. This is essentially the invisible handmechanism of Adam Smith's in an ecological context. What we demonstrate is for ideal systems, similar to the ideal gas or Ising model in thermodynamics. The next steps would involve examining and learning how real swarms behave compared to their ideal versions. Our theory is not limited to just birds flocking but can be adapted for the self-organizing dynamics of other active matter systems.

Field-theoretic analysis of directed percolation: Three-loop approximation.

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study this model by means of the field-theoretic formulation with a subsequent renormalization group analysis. We calculate all critical exponents needed for the quantitative description of the corresponding universality class to the third order in perturbation theory. Using dimensional regularization with minimal subtraction scheme, we carry out perturbative calculations in a formally small parameter ɛ, where ɛ=4-d is a deviation from the upper critical dimension d_{c}=4. We use a nontrivial combination of analytical and numerical tools in order to determine ultraviolet divergent parts of Feynman diagrams.

Infinite-randomness criticality in monitored quantum dynamics with static disorder

The measurement-induced phase transition (MIPT) represents a critical point connected to quantum information and nonequilibrium statistical physics. However, any quantum code utilizing the MIPT can be affected by noise introduced in device fabrication, appearing as static disorder. Leveraging analytics and large-scale simulations, the authors show that this static noise destabilizes the MIPT towards an infinite-randomness critical point. Their findings reveal the Harris criterion's applicability beyond equilibrium, indicating the relevance of perturbations at this phase transition.

Paradoxical nature of negative mobility in the weak dissipation regime.

We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time-periodic force and a static bias. In doing so, we focus on the negative mobility phenomenon in which the average velocity of the particle is opposite to the constant force acting on it. Surprisingly, we find that in the weak dissipation regime, thermal fluctuations induce negative mobility much more frequently than it happens if dissipation is stronger. In particular, for the very first time, we report a parameter set in which thermal noise causes this effect in the nonlinear response regime. Moreover, we show that the coexistence of deterministic negative mobility and chaos is routinely encountered when approaching the overdamped limit in which chaos does not emerge rather than near the Hamiltonian regime of which chaos is one of the hallmarks. On the other hand, at non-zero temperature, the negative mobility in the weak dissipation regime is typically affected by weak ergodicity breaking. Our findings can be corroborated experimentally in a multitude of physical realizations, including, e.g., Josephson junctions and cold atoms dwelling in optical lattices.

Nonequilibrium statistical physics beyond the ideal heat bath approximation.

Important models of nonequilibrium statistical physics (NESP) are limited by a commonly used, but often unrecognized, near-equilibrium approximation. Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion models, and the Schnakenberg model of biochemical networks suppose that fluctuations are due to an ideal equilibrium bath. But far from equilibrium, this perfect bath concept does not hold. A more principled approach should derive the rate fluctuations from an underlying dynamical model, rather than assuming a particular form. Here, using maximum caliber as the underlying principle, we derive corrections for NESP processes in an imperfect-but more realistic-environment, corrections which become particularly important for a system driven strongly away from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of its temperature, the bath's speed and size must also be used to characterize the bath's ability to handle fast or large fluctuations.

Phononic thermal conduction and thermal regulation in low-dimensional micro-nano scale systems: Nonequilibrium statistical physics problems from chip heat dissipation

“Heat death”, namely, overheating, which will deteriorate the function of chips and eventually burn the device and has become an obstacle in the roadmap of the semiconductor industry. Therefore, heat dissipation becomes a key issue in further developing semiconductor. Heat conduction in chips encompasses the intricate dynamics of phonon conduction within one-dimensional, two-dimensional materials, as well as the intricate phonon transport through interfaces. In this paper, the research progress of the complexities of phonon transport on a nano and nanoscale in recent three years, especially the size dependent phonon thermal transport and the relationship between anomalous heat conduction and anomalous diffusion are summarized. Further discussed in this paper is the fundamental question within non-equilibrium statistical physics, particularly the necessary and sufficient condition for a given Hamiltonian whose macroscopic transport behavior obeys Fourier’s law. On the other hand, the methods of engineering the thermal conduction, encompassing nanophononic crystals, nanometamaterials, interfacial phenomena, and phonon condensation are also introduced. In order to comprehensively understand the phononic thermal conduction, a succinct overview of phonon heat transport phenomena, spanning from thermal quantization and the phonon Hall effect to the chiral phonons and their intricate interactions with other carriers is presented. Finally, the challenges and opportunities, and the potential application of phonons in quantum information are also discussed.

Entropy rate of random walks on complex networks under stochastic resetting.

Stochastic processes under resetting at random times have attracted a lot of attention in recent years and served as illustrations of nontrivial and interesting static and dynamic features of stochastic dynamics. In this paper, we aim to address how the entropy rate is affected by stochastic resetting in discrete-time Markovian processes, and we explore nontrivial effects of the resetting in the mixing properties of a stochastic process. In particular, we consider resetting random walks (RRWs) with a single resetting node on three different types of networks: degree-regular random networks, a finite-size Cayley tree, and a Barabási-Albert (BA) scale-free network, and we compute the entropy rate as a function of the resetting probability γ. Interestingly, for the first two types of networks, the entropy rate shows a nonmonotonic dependence on γ. There exists an optimal value of γ at which the entropy rate reaches a maximum. Such a maximum is larger than that of maximal-entropy random walks (MREWs) and standard random walks (SRWs) on the same topology, while for the BA network the entropy rate of RRWs either shows a unique maximum or decreases monotonically with γ, depending upon the choice of the resetting node. When the maximum entropy rate of RRWs exists, it can be higher or lower than that of MREWs or SRWs. Our study reveals a nontrivial effect of stochastic resetting on nonequilibrium statistical physics.

Towards a statistical physics of dating apps

Over the last ten years, a sharp rise in the number of dating apps has broadened the spectrum of how one can get in contact with new acquaintances. A common feature of such apps is a swipe, enabling a user to decide whether to like or dislike another user. As is the case in real life, a user may be more or less popular, which implies that the distribution of likes among different users is broad. In this paper, we show how likes are distributed across users, based on different decision-making strategies, app settings and their feedback. We apply theoretical methods originally developed in non-equilibrium statistical physics to investigate the dynamics of dating app networks. More specifically, we show that whenever a dating app differentially displays users with respect to their popularity, users are split into two categories: a first category including users who have received the most likes and a second category, referred to as a condensate, which in long-term will be reduced to a small fraction of likes or to no likes at all. Finally, we explore realist models based on a rating system of the users, known as Elo. These models will turn out to exhibit behaviour typical of gelating systems, characterized by a bimodal distribution of likes among the users with broad tails. Altogether, we provide a minimal theoretical framework to infer statistical observables in social networks governed by coupled internal states.

On the Nature of Information: How FAIR Digital Objects are Building-up Semantic Space

On the Nature of Information: How FAIR Digital Objects are Building-up Semantic Space

Floquet States in Open Quantum Systems

In Floquet engineering, periodic driving is used to realize novel phases of matter that are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe for obtaining a static effective Hamiltonian. Although many existing works have treated closed systems, it is important to consider the effect of dissipation, which is ubiquitous in nature. Understanding the interplay of periodic driving and dissipation is a fundamental problem of nonequilibrium statistical physics that is receiving growing interest because of the fact that experimental advances have allowed us to engineer dissipation in a controllable manner. In this review, we give a detailed exposition on the formalism of quantum master equations for open Floquet systems and highlight recent work investigating whether equilibrium statistical mechanics applies to Floquet states.