System In Nonequilibrium Steady State Research Articles

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation.

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional (8D) limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

First and second laws of information processing by nonequilibrium dynamical states.

The averaged steady-state surprisal links a driven stochastic system's information processing to its nonequilibrium thermodynamic response. By explicitly accounting for the effects of nonequilibrium steady states, a decomposition of the surprisal results in an information processing first law that extends and tightens-to strict equalities-various information processing second laws. Applying stochastic thermodynamics' integral fluctuation theorems then shows that the decomposition reduces to the second laws under appropriate limits. In unifying them, the first law paves the way to identifying the mechanisms by which nonequilibrium steady-state systems leverage information-bearing degrees of freedom to extract heat. To illustrate, we analyze an autonomous Maxwellian information ratchet that tunably violates detailed balance in its effective dynamics. This demonstrates how the presence of nonequilibrium steady states qualitatively alters an information engine's allowed functionality.

Discovering a Local Fluctuation Theorem with Machine Learning

A groundbreaking study reveals a new time-local fluctuation theorem using machine learning, revolutionizing our understanding of deterministic nonequilibrium steady state systems.

Absence and recovery of cost-precision tradeoff relations in quantum transport

The operation of many classical and quantum systems in nonequilibrium steady state is constrained by cost-precision (dissipation-fluctuation) tradeoff relations, delineated by the thermodynamic uncertainty relation (TUR). However, coherent quantum electronic nanojunctions can escape such a constraint, showing finite charge current and nonzero entropic cost with vanishing current fluctuations. Here we analyze the absence, and restoration, of cost-precision tradeoff relations in fermionic nanojunctions under different affinities: voltage and temperature biases. With analytic work and simulations, we show that both charge and energy currents can display the absence of cost-precision tradeoffs if we engineer the transmission probability as a boxcar function---with a perfect transmission and hard energy cutoffs. Specifically for charge current under voltage bias, the standard TUR may be immediately violated as we depart from equilibrium, and it is exponentially suppressed with increased voltage. However, beyond idealized, hard-cutoff energy-filtered transmission functions, we show that realistic models with soft cutoffs or imperfect transmission functions follow cost-precision tradeoffs and eventually recover the standard TUR sufficiently far from equilibrium. The existence of cost-precision tradeoff relations is thus suggested as a generic feature of realistic nonequilibrium quantum transport junctions.

An Active Inference Model of Collective Intelligence.

Collective intelligence, an emergent phenomenon in which a composite system of multiple interacting agents performs at levels greater than the sum of its parts, has long compelled research efforts in social and behavioral sciences. To date, however, formal models of collective intelligence have lacked a plausible mathematical description of the relationship between local-scale interactions between autonomous sub-system components (individuals) and global-scale behavior of the composite system (the collective). In this paper we use the Active Inference Formulation (AIF), a framework for explaining the behavior of any non-equilibrium steady state system at any scale, to posit a minimal agent-based model that simulates the relationship between local individual-level interaction and collective intelligence. We explore the effects of providing baseline AIF agents (Model 1) with specific cognitive capabilities: Theory of Mind (Model 2), Goal Alignment (Model 3), and Theory of Mind with Goal Alignment (Model 4). These stepwise transitions in sophistication of cognitive ability are motivated by the types of advancements plausibly required for an AIF agent to persist and flourish in an environment populated by other highly autonomous AIF agents, and have also recently been shown to map naturally to canonical steps in human cognitive ability. Illustrative results show that stepwise cognitive transitions increase system performance by providing complementary mechanisms for alignment between agents’ local and global optima. Alignment emerges endogenously from the dynamics of interacting AIF agents themselves, rather than being imposed exogenously by incentives to agents’ behaviors (contra existing computational models of collective intelligence) or top-down priors for collective behavior (contra existing multiscale simulations of AIF). These results shed light on the types of generic information-theoretic patterns conducive to collective intelligence in human and other complex adaptive systems.

Thermodynamic vs statistical entropy production in thermostatted Hamiltonian dynamics

Sufficient conditions were recently established for the rates of thermodynamic entropy production and phase space volume contraction to be identically equal in thermostatted Hamiltonian systems in non-equilibrium steady states (Ramshaw 2017 Phys. Rev. E 96 052122). This equality has previously been interpreted as a statistical analogue of the second law of thermodynamics (SLT). However, that interpretation is unjustified because the volume contraction rate represents the production rate of the statistical entropy of the system and thermostat together, which differs in general from that of the Hamiltonian system itself. This logical lacuna is remedied by identifying two further conditions which combine with the previous conditions to imply a proper statistical analogue of the SLT. The first of these new conditions can simply be imposed a priori, whereas the second, like ergodicity and mixing, involves the asymptotic statistical properties of the dynamics as t → ∞. The latter condition seems likely to be analytically intractable in general, and therefore to require numerical investigation and confirmation in systems of practical interest.

Modules or Mean-Fields?

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

Synchronization along quantum trajectories

We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol oscillators interacting through dissipative coupling. We show the deep impact of synchronization on the statistics of phase-locking indicators and other correlation measures defined for single trajectories, spotting a link between the presence of synchronization and the emergence of large tails in the probability distribution for the entanglement along trajectories. Our results shed new light on fundamental issues regarding quantum synchronization providing new methods for its precise quantification.

On the possible distributions of temperature in nonequilibrium steady states

Superstatistics is a framework in nonequilibrium statistical mechanics that successfully describes a wide variety of complex systems, including hydrodynamic turbulence, weakly-collisional plasmas, cosmic rays, power grid fluctuations, among several others. In this work we analyze the class of nonequilibrium steady-state systems consisting of a subsystem and its environment, and where the subsystem is described by the superstatistical framework. In this case we provide an answer to the mechanism by which a broad distribution of temperature arises, namely due to correlation between subsystem and environment. We prove that there is a unique microscopic definition of inverse temperature compatible with superstatistics, in the sense that all moments of and coincide. The function however, cannot depend on the degrees of freedom of the system itself, only on the environment, in full agreement with our previous impossibility theorem (Davis and Gutiérrez 2018 Physica A 505 864–70). The present results also constrain the possible joint ensembles of system and environment compatible with superstatistics.

Quantum response theory for nonequilibrium steady states

Quantum response theory is a cornerstone of statistical physics. However, the standard Kubo formalism is restricted to isolated equilibrium systems. We here generalize Kubo's results to open quantum systems in nonequilibrium steady states. We derive three different, but equivalent, forms of the quantum response function. We discuss for each of them the role of the noncommutativity of quantum operators and introduce a steady-state extension of the Kubo transformation. We show in particular that the equilibrium response vanishes for perturbations that commute with the unperturbed Hamiltonian, while the steady-state response does not, highlighting the profound difference between the two linear response theories.Received 10 December 2018DOI:https://doi.org/10.1103/PhysRevResearch.1.033156Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsQuantum statistical mechanicsStatistical PhysicsGeneral Physics

Thermodynamic integration for the determination of nonequilibrium entropy

Planar shear flow described by the SLLOD algorithm is a well-defined nonequilibrium steady state system with strong nonlinearity. Equipped with a numerical feedback thermostat it produces stable averages and fluctuations. We assume that moving infinitely slowly and isoenergetically along nonequilibrium states the excess rate at which heat is removed from the system can determine the work needed to move the system from equilibrium to steady states far from equilibrium. The excess heat rate is measured relative to the average heat rate of the corresponding steady state. As the best approximation, we use the configurational temperature to obtain entropy from the excess work in the typical shear rate range of simulations.

Langevin equation for systems with a preferred spatial direction.

In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by an external force and alters the Gaussian structure of the system's fluctuations. In addition, by solving this extended equation, we provide a physical interpretation for the statistical properties of the fluctuations in these systems. Connections of the extended Langevin equation with the theory of active Brownian motion are discussed as well.

Approximating the entire spectrum of nonequilibrium steady-state distributions using relative entropy: An application to thermal conduction.

Distribution functions for systems in nonequilibrium steady states are usually determined through detailed experiments, both in numerical and real-life settings in the laboratory. However, for a protocol-driven distribution function, it is usually prohibitive to perform such detailed experiments for the entire range of the protocol. In this article we show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowly varying protocol can be accurately obtained from limited data and the closest known detailed state of the system. In this manner, one needs to perform only a few detailed experiments to obtain the nonequilibrium distribution function for the entire gamut of nonlinearity. We achieve this by maximizing the relative entropy functional (MaxRent) subject to constraints supplied by the problem definition and new measurements. MaxRent is found to be superior to the principle of maximum entropy (MaxEnt), which maximizes Shannon's informational entropy for estimating distributions but lacks the ability to incorporate additional prior information. The MaxRent principle is illustrated using a toy model of ϕ4 thermal conduction consisting of a single lattice point. An external protocol controlled position-dependent temperature field drives the system out of equilibrium. Two different thermostatting schemes are employed: the Hoover-Holian deterministic thermostat (which produces multifractal dynamics under strong nonlinearity) and the Langevin stochastic thermostat (which produces phase-space-filling dynamics). Out of the 80 possible states produced by the protocol, we assume that four states are known to us in detail, one of which is used as input into MaxRent at a time. We find that MaxRent approximates the phase-space density functions for every value of the protocol, even when they are far from the known distribution. MaxEnt, however, is unable to capture the fine details of the phase-space distribution functions. We expect this method to be useful in other external protocol-driven nonequilibrium cases as well, making it unnecessary to perform detailed experiments for all values of the protocol when one wishes to obtain approximate distributions.

Experimental study of energy transport between two granular gas thermostats

We report on the energy transport between two coupled probes in contact with granular thermostats at different temperatures. In our experiment, two identical blades, which are electromechanically coupled, are immersed in two granular gases maintained in different non-equilibrium stationary states, characterized by different temperatures. First, we show that the energy flux from one probe to another is, in temporal average, proportional to the temperature difference, as in the case of equilibrium thermostats. Secondly, we observe that the instantaneous flux is highly intermittent and that fluctuations exhibit an asymmetry which increases with the temperature difference. Interestingly, this asymmetry, related to irreversibility, is correctly accounted for by a relation strongly evoking the Fluctuation Theorem. Our experiment is a simple macroscopic realisation, suitable for the study of energy exchanges between systems in non-equilibrium steady states.

Anomalous preasymptotic colloid transport by hydrodynamic dispersion in microfluidic capillary flow.

The anomalous preasymptotic transport of colloids in a microfluidic capillary flow due to hydrodynamic dispersion is measured by noninvasive nuclear magnetic resonance (NMR). The data indicate a reduced scaling of mean squared displacement with time from the 〈z(t)(2)〉(c) ∼ t(3) behavior for the interaction of a normal diffusion process with a simple shear flow. This nonequilibrium steady-state system is shown to be modeled by a continuous time random walk (CTRW) on a moving fluid. The full propagator of the motion is measured by NMR, providing verification of the assumption of Gaussian jump length distributions in the CTRW model. The connection of the data to microrheology measurements by NMR, in which every particle in a suspension contributes information, is established.

Fluctuation-dissipation theorem for chiral systems in nonequilibrium steady states

We consider a three-terminal system with a chiral edge channel connecting the source and drain terminals. Charge can tunnel between the chiral edge and a third terminal. The third terminal is maintained at a different temperature and voltage than the source and drain. We prove a general relation for the current noises detected in the drain and third terminal. It has the same structure as an equilibrium fluctuation-dissipation relation with the nonlinear response in place of the linear conductance. The result applies to a general chiral system and can be useful for detecting "upstream" modes on quantum Hall edges.

Nonequilibrium Steady States in Contact: Approximate Thermodynamic Structure and Zeroth Law for Driven Lattice Gases

We explore driven lattice gases for the existence of an intensive thermodynamic variable which could determine "equilibration" between two nonequilibrium steady-state systems kept in weak contact. In simulations, we find that these systems satisfy surprisingly simple thermodynamic laws, such as the zeroth law and the fluctuation-response relation between the particle-number fluctuation and the corresponding susceptibility remarkably well. However, at higher densities, small but observable deviations from these laws occur due to nontrivial contact dynamics and the presence of long-range spatial correlations.

Nonequilibrium Fock space for the electron transport problem

Based on the formalism of thermofield dynamics we propose a concept of nonequilibrium Fock space and nonequilibrium quasiparticles for quantum many-body system in nonequilibrium steady state. We develop a general theory as well as demonstrate the utility of the approach on the example of electron transport through the interacting region. The proposed approach is compatible with advanced quantum chemical methods of electronic structure calculations such as coupled cluster theory and configuration interaction.

Noise-induced oscillations in non-equilibrium steady state systems

We consider the effect of stochastic sources on the self-organization process being initiated with creation of the limit cycle. The general expressions obtained are applied to the stochastic Lorenz system to show that offset from the equilibrium steady state can destroy the limit cycle at a certain relation between characteristic scales of temporal variation of principal variables. Noise-induced resonance related to the limit cycle is found analytically to appear in the non-equilibrium steady state system if the fastest variations display a principal variable, which is coupled with two different degrees of freedom or more.

Statistical mechanical theory for the structure of steady state systems: application to a Lennard-Jones fluid with applied temperature gradient.

The constrained entropy and probability distribution are given for the structure that develops in response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory is linear but is applicable to gradients with arbitrary spatial variation. The phase space probability distribution is also given, and it is surprisingly simple with a straightforward physical interpretation. With it, all of the known methods of equilibrium statistical mechanics for inhomogeneous systems may now be applied to determining the structure of nonequilibrium steady state systems. The theory is illustrated by performing Monte Carlo simulations on a Lennard-Jones fluid with externally imposed temperature and chemical potential gradients. The induced energy and density moments are obtained, as well as the moment susceptibilities that give the rate of change of these with imposed gradient and which also give the fluctuations in the moments. It is shown that these moment susceptibilities can be written in terms of bulk susceptibilities and also that the Soret coefficient can be expressed in terms of them.