Nonequilibrium Fluctuations Research Articles

Nonequilibrium phenomena in driven and active Coulomb field theories

The classical Coulomb gas model has served as one of the most versatile frameworks in statistical physics, connecting a vast range of phenomena across many different areas. Nonequilibrium generalisations of this model have so far been studied much more scarcely. With the abundance of contemporary research into active and driven systems, one would naturally expect that such generalisations of systems with long-ranged Coulomb-like interactions will form a fertile playground for interesting developments. Here, we present two examples of novel macroscopic behaviour that arise from nonequilibrium fluctuations in long-range interacting systems, namely (1) unscreened long-ranged correlations in strong electrolytes driven by an external electric field and the associated fluctuation-induced forces in the confined Casimir geometry, and (2) out-of-equilibrium critical behaviour in self-chemotactic models that incorporate the particle polarity in the chemotactic response of the cells. Both of these systems have nonlocal Coulomb-like interactions among their constituent particles, namely, the electrostatic interactions in the case of the driven electrolyte, and the chemotactic forces mediated by fast-diffusing signals in the case of self-chemotactic systems. The results presented here hint to the rich phenomenology of nonequilibrium effects that can arise from strong fluctuations in Coulomb interacting systems, and a rich variety of potential future directions, which are discussed.

Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems.

Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet’s acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate G within a few . Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime.

Nonequilibrium fluctuations and nonlinear response of an active bath

We analyze the dynamics of a passive colloidal probe immersed in an active bath using an optical trap to study three physical processes: (1) the non-equilibrium fluctuations transferred to the probe by the active bath, (2) the friction experienced by the probe as it is driven through the active bath, and (3) the force relaxation of the probe returning to its equilibrium position. We measure the local force dynamics where all of the following characteristics are of $\mathcal{O}(1)$: the size of the probe colloid relative to active bath particle; the size of the probe colloid relative to the characteristic run-length of an active particle; and the timescale of probe movement to the persistence time of an active particle. We find at P\'{e}clet (Pe) $\ll 1$ the active suspension exhibits shear thinning down to the solvent viscosity (but not below); at $0.85 <$ Pe $\leq 5.1$ the active bath shear thickens; and at Pe $\geq 8.5$ the effective viscosity of the active bath shows a decreased effect of thickening and plateaus. These results are in agreement with recent modeling and simulations of the nonlinear rheology of an isotropic active bath, providing experimental verification, and suggesting the model predictions extends to moderately dense suspensions. Further, we observe that the distribution of force fluctuations depends on Pe, unlike in passive equilibrium baths. Lastly, we measure the energy transfer rate from the active bath to the probe to be $\langle J \rangle \approx 10^3$ $k_B T/$s, which leads to an increase in the effective diffusion of the probe by a factor of $\sim 2$.

Spontaneous self-propulsion and nonequilibrium shape fluctuations of a droplet enclosing active particles

Active particles, such as swimming bacteria or self-propelled colloids, spontaneously assemble into large-scale dynamic structures. Geometric boundaries often enforce different spatio-temporal patterns compared to unconfined environment and thus provide a platform to control the behavior of active matter. Here, we report collective dynamics of active particles enclosed by soft, deformable boundary, that is responsive to the particles’ activity. We reveal that a quasi two-dimensional fluid droplet enclosing motile colloids powered by the Quincke effect (Quincke rollers) exhibits strong shape fluctuations with a power spectrum consistent with active fluctuations driven by particle-interface collisions. A broken detailed balance confirms the nonequilibrium nature of the shape dynamics. We further find that rollers self-organize into a single drop-spanning vortex, which can undergo a spontaneous symmetry breaking and vortex splitting. The droplet acquires motility while the vortex doublet exists. Our findings provide insights into the complex collective behavior of active colloidal suspensions in soft confinement.

Nonlinearities in shadowgraphy experiments on non-equilibrium fluctuations in polymer solutions

Giant thermal and solutal non-equilibrium fluctuations are observed in shadowgraphy experiments on liquid mixtures subjected to a temperature gradient. For large temperature differences, both the temperature and the composition dependence of the relevant thermophysical parameters and the nonlinear terms in the diffusion equation need to be taken into account, leading to a nonlinear concentration profile. For temperature differences exceeding the inverse of the Soret coefficient, in our example approximately 10 K, the usual data evaluation yields increasingly wrong diffusion and Soret coefficients that are off by almost a factor of two for a temperature difference of 50 K. A local model that treats the measured shadowgraph signal as a superposition of the contributions from every layer of the sample is able to capture the essential trend and yields a good agreement with experimental data. The results are important for the application of shadowgraphy as a tool for the measurement of Soret and diffusion coefficients, where large temperature gradients promise a good signal-to-noise ratio.Graphical abstract

Wading through the void: Exploring quantum friction and nonequilibrium fluctuations

When two or more objects move relative to one another in vacuum, they experience a drag force, which, at zero temperature, usually goes under the name of quantum friction. This contactless non-conservative interaction is mediated by the fluctuations of the material-modified quantum electrodynamic vacuum and, hence, is purely quantum in nature. Numerous investigations have revealed the richness of the mechanisms at work, thereby stimulating novel theoretical and experimental approaches and identifying challenges and opportunities. In this Perspective, we provide an overview of the physics surrounding quantum friction and a perspective on recent developments.

Open quantum system dynamics and the mean force Gibbs state

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and energies of the system. However, at decreasing system sizes, i.e., for nanoscale and quantum systems, the interaction with their environments is not negligible. The question then arises: Is the system's steady state still the Gibbs state? If not, how may the steady state depend on the interaction details? Here, we provide an overview of recent progress on answering these questions. We expand on the state of the art along two general avenues: First, we take the static point-of-view, which postulates the so-called mean force Gibbs state. This view is commonly adopted in the field of strong coupling thermodynamics, where modified laws of thermodynamics and nonequilibrium fluctuation relations are established on the basis of this modified state. Second, we take the dynamical point of view, originating from the field of open quantum systems, which examines the time-asymptotic steady state within two paradigms. We describe the mathematical paradigm, which proves return to equilibrium, i.e., convergence to the mean force Gibbs state, and then discuss a number of microscopic physical methods, particularly master equations. We conclude with a summary of established links between statics and equilibration dynamics and provide an extensive list of open problems. This comprehensive overview will be of interest to researchers in the wider fields of quantum thermodynamics, open quantum systems, mesoscopic physics, statistical physics, and quantum optics and will find applications whenever energy is exchanged on the nanoscale, from quantum chemistry and biology to magnetism and nanoscale heat management.

Mass diffusion and Soret coefficient measurements of triethylene glycol/water binary mixtures by dynamic shadowgraphy.

The investigation of the transport properties of binary fluid mixtures remains a topic of interest in relation to the more challenging studies of ternary mixtures. In fact, the study of the phase boundary limits of the Gibbs composition triangle can be the initial step for a more complete analysis of ternary mixtures. In this paper, we apply the dynamic shadowgraphy optical technique to study non-equilibrium fluctuations induced by the presence of a gradient of temperature and/or concentration in the triethylene glycol (TEG)/water system. These thermodiffusion and free-diffusion experiments aim at measuring the transport properties of samples of the studied system at different experimental conditions. We scan both the average temperature and the TEG concentration, which allows us investigating both positive and negative thermodiffusive behaviours. The obtained values of mass diffusion coefficient are consistent with data available in the literature in the range of temperature investigated in this study. The mass diffusion coefficient of the sample prepared at 0.7 w/w TEG concentration are characterised by shadowgraphy following the two proposed methods, exhibiting consistent results. An increase of the mass diffusion coefficient as a function of the average temperature is highlighted. On the other hand, the thermodiffusion coefficient appears to be independent of the average temperature of the sample at 0.3 w/w TEG concentration.

Emergent Kardar-Parisi-Zhang Phase in Quadratically Driven Condensates.

In bosonic gases at thermal equilibrium, an external quadratic drive can induce a Bose-Einstein condensation described by the Ising transition, as a consequence of the explicitly broken U(1) phase rotation symmetry down to Z_{2}. However, in physical realizations such as exciton polaritons and nonlinear photonic lattices, thermal equilibrium is lost and the state is rather determined by a balance between losses and external drive. A fundamental question is then how nonequilibrium fluctuations affect this transition. Here, we show that in a two-dimensional driven-dissipative Bose system the Ising phase is suppressed and replaced by a nonequilibrium phase featuring Kardar-Parisi-Zhang (KPZ) physics. Its emergence is rooted in a U(1)-symmetry restoration mechanism enabled by the strong fluctuations in reduced dimensionality. Moreover, we show that the presence of the quadratic drive term enhances the visibility of the KPZ scaling, compared to two-dimensional U(1)-symmetric gases, where it has remained so far elusive.

Hydrodynamics of the Generalized N-urn Ehrenfest Model

In this paper we are concerned with a generalized N-urn Ehrenfest model, where balls perform independent random walks between N boxes uniformly laid on [0,1]. After a proper scaling of the transition rates function of the aforesaid random walk, we derive the hydrodynamic limit of the model, i.e., the law of large numbers which the empirical measure of the model follows, under an assumption where the initial number of balls in each box independently follows a Poisson distribution. We show that the empirical measure of the model converges weakly to a deterministic measure with density driven by an integral equation. Furthermore, we derive non-equilibrium fluctuation of the model, i.e, the central limit theorem from the above hydrodynamic limit. We show that the non-equilibrium fluctuation of the model is driven by a time-inhomogeneous generalized O-U process on the dual of C[0,1]. At last, we prove a large deviation principle from the hydrodynamic limit under an assumption where the transition rates function from [0,1] × [0,1] to $[0, +\infty )$ of the aforesaid random walk is a product of two marginal functions from [0,1] to $[0, +\infty )$ .

Controlling anisotropy in 2D microscopic models of growth

The quantitative knowledge of interface anisotropy in lattice models is a major issue, both for the parametrization of continuum interface models, and for the analysis of experimental observations. In this paper, we focus on the anisotropy of line tension and stiffness, which plays a major role both in equilibrium shapes and fluctuations, and in the selection of nonequilibrium growth patterns. We consider a 2D Ising Hamiltonian on a square lattice with first and second-nearest-neighbor interactions. The surface stiffness and line tension are calculated by means of a broken-bond model for arbitrary orientations. The analysis of the interface energy allows us to determine the conditions under which stiffness anisotropy is minimal. These results are supported by a quantitative comparison with kinetic Monte Carlo simulations, based on the coupling of a field of mobile atoms to a condensed phase. Furthermore, we introduce a generic smoothing parameter which allows one to mimic the finite resolution of experimental microscopy techniques. Our results provide a method to fine-tune the interface energy in models of nanoscale non-equilibrium processes, where anisotropy and fluctuations combine and give rise to non-trivial morphologies.

Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies.

A universal large N theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse-grained thermodynamic uncertainty relations-one of them being an activity bound. Importantly, the activity serves as a tighter bound for the entropy production in 1D systems. These results are particularly useful in the many-body regime, where typically a coarse-grained approach is required to handle the large microscopic state space.

Near-Field Energy Transfer between Graphene and Magneto-Optic Media.

We consider the near-field radiative energy transfer between two separated parallel plates: graphene supported by a substrate and a magneto-optic medium. We first study the scenario in which the two plates have the same temperature. An electric current through the graphene gives rise to nonequilibrium fluctuations and induces energy transfer. Both the magnitude and direction of the energy flux can be controlled by the electric current and an in-plane magnetic field in the magneto-optic medium. This is due to the interplay between the nonreciprocal photon occupation number in the graphene and nonreciprocal surface modes in the magneto-optic plate. Furthermore, we report that a tunable thermoelectric current can be generated in the graphene in the presence of a temperature difference between the two plates.

Stochastic Thermodynamics of Nonlinear Electronic Circuits: A Realistic Framework for Computing Around kT

We provide a general theory of nonlinear electronic circuits subjected to thermal noise. The devices constituting the circuit can have arbitrary I−V curves but must display shot noise. This theory includes tunnel junctions, diodes, and MOS transistors in subthreshold operation, among others. The stochastic nonequilibrium thermodynamics of these circuits is also established. The irreversible entropy production is expressed in terms of thermodynamic potentials and forces, and its fluctuations satisfy fluctuation theorems. Our theory is ideally suited to formulate a thermodynamics of computing with realistic architectures, where the reduction in transistor size and operating voltages make thermal fluctuations increasingly important. We demonstrate this point in two ways: first, by proposing a stochastic model of a CMOS inverter whose actual transfer function deviates from the deterministic one due to nonequilibrium fluctuations, and, second, by proposing a low-power full-CMOS design for a probabilistic bit (or binary stochastic neuron) exploiting intrinsic noise.8 MoreReceived 1 October 2020Revised 2 July 2021Accepted 8 July 2021DOI:https://doi.org/10.1103/PhysRevX.11.031064Published 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 & irreversible thermodynamicsThermodynamicsThermodynamics of computationPhysical SystemsStochastic dynamical systemsStochastic networksStatistical PhysicsNonlinear DynamicsCondensed Matter, Materials & Applied PhysicsNetworks

Self-pulsing discharge in hollow cathode simulated by a fluid model

A fluid model without an external circuit is used in simulating self-pulses in hollow cathode discharge under a He-Ar gas at 10 Torr. The average discharge current increases with anode potential, and three types of self-pulsing discharge modes are obtained: (a) regular self-pulse, (b) low amplitude self-pulse, and (c) damped oscillating pulses modes. The temporal and spatial distributions of plasma parameters in the self-pulsing discharge mode are studied. Results show that the electron density, electric potential, electric field, total net electron production rates integrated over the entire discharge cell and net positive charge density change periodically in a self-pulsing period. Self-pulsing frequency ranges from tens of kHz to more than 100 kHz, and increases linearly with the average discharge current approximately. In the present average discharge current range, the peak value and current amplitude of pulsing current increases and then decreases with the increasing average current, whereas the minimum pulsing current consistently increases. The change trend of extreme self-pulsing discharge current is consistent with the change trends of total net electron production rate and net positive charge density in the discharge space. Finally, the mechanism of self-pulse in a hollow cathode discharge is proposed. Simulated results show that the phases of different plasma parameters are different in different discharge regions in a self-pulsing period. Non-equilibrium fluctuation of plasma parameters in different discharge regions is one of important factors in the formation of self-pulse. Self-pulse does not depend on an external circuit and originates from the internal microcosmic mechanism of discharge: the enhancement and weakening of the positive charge layer.

Ratchet universality in coupled dissipative oscillators without external bias.

Directed ratchet transport is generally observed in nonautonomous systems as a result of the interplay of nonlinearity, symmetry breaking, and nonequilibrium fluctuations. Here we demonstrate that ratchet dynamics can appear in significant transporting degrees of freedom of dissipative coupled systems without external bias due to unidirectional coupling of oscillatory degrees of freedom (which are also nonbiasing in any direction), while optimal enhancement of directed ratchet transport occurs when the initial conditions and parameters of such ratcheting degrees of freedom are suitably chosen as predicted by the theory of ratchet universality. The simple case of linear oscillatory degrees of freedom is discussed in detail, and numerical experiments are described which confirm all the theoretical predictions, including the dependence of current (velocity) reversals on the initial conditions and the ratcheting degrees-of-freedom parameters. This autonomous ratchet scenario could be exploited technologically, for instance, in the context of noncontact, rack-and-pinion type, nanoscale setups with coupling from the lateral Casimir force, and is relevant for studies of molecular motors in the biological realm.

Nonequilibrium fractional correlation functions and fluctuation–dissipation in linear viscoelasticity

A simple model for time retarded fractional density and velocity hydrodynamic fluctuations correlations of a linear viscoelastic fluid under an external gradient is proposed. A fractional generalized Langevin equation with a Caputo’s fractional time derivative is formulated for a power-law memory kernel with long correlation noise. The fractional density and velocity fluctuations correlation functions, as well as the fractional light scattering spectra, and the fractional intermediate scattering function (FISF) are calculated analytically for power-law viscoelasticity. Their relation to the longitudinal modulus of the viscoelastic fluid is also obtained. We find that for different frequency intervals appropriate to perform isothermal light scattering experiments using Fabry–Perot interferometry and photon correlation, the non-equilibrium fractional structure factor may be smaller or larger than its fractional equilibrium values. We also discuss the validity of a fractional fluctuation–dissipation theorem for this model in terms of the asymptotic behavior of the equilibrium fractional correlation functions of the model.

Transient fluctuation-induced forces in driven electrolytes after an electric field quench

Understanding how electrolyte solutions behave out of thermal equilibrium is a long-standing endeavor in many areas of chemistry and biology. Although mean-field theories are widely used to model the dynamics of electrolytes, it is also important to characterize the effects of fluctuations in these systems. We have recently shown that the dynamics of the ions in a strong electrolyte that is driven by an external electric field can generate long-ranged correlations manifestly different from the equilibrium screened correlations; in the nonequilibrium steady state, these correlations give rise to a novel long-range fluctuation-induced force (FIF). Here, we extend the Langevin analysis of the FIF by considering the dynamics of a strong electrolyte after it is quenched from thermal equilibrium by a constant electric field. We show that the asymptotic long-distance limit of both of the charge and density correlation functions is long-ranged and generally diffusive in time. These correlations give rise to long-ranged FIFs acting on uncharged confining plates with long-time regimes that are governed by slow power-law temporal decays toward the steady-state value of the force amplitude; at early times, the temporal variations of the FIF are non-monotonic with possible sign changes in some parameter regimes. These findings show that nonequilibrium fluctuations have nontrivial implications on the dynamics of objects immersed in a driven electrolyte, and they could be useful for exploring new ways of controlling long-distance forces in charged solutions.

Temperature-Frequency Controlling the Characteristics of a Pulsating Brownian Ratchet with Slightly Fluctuating Potential Energy

Within the approximation of slight fluctuations of the nanoparticle potential energy, we developed a method for calculating the characteristics of a Brownian ratchet (a complex nonlinear system capable of extracting useful work from unbiased nonequilibrium fluctuations). The method is suitable for studying the mechanisms and modes of functioning of artificial nanomotors. Unlike the effort-consuming obtaining and applying for this studying the Green's functions of the coordinate representation which describe diffusion in the stationary component of the potential, the proposed method operates with the Fourier representation of both the control and desired functions. That allows calculating the Green's functions as inverse matrices in the space of Fourier harmonics and finding the average velocity of a Brownian ratchet with an arbitrary spatial and temporal dependence of the potential energy. To illustrate the method, an analysis has been performed of the functioning of a ratchet in which the directional motion of nanoparticles arises due to small stochastic fluctuations of an asymmetric sawtooth potential profile with an arbitrary barrier-heightto- thermal-energy ratio. It is shown that, with a harmonic coordinate dependence of these fluctuations, a change in the direction and intensity of the ratchet effect is controlled not only by tuning the magnitude of their phase shift relative to the sawtooth potential (the fact revealed before in the high-temperature approximation), but also by changing the temperature and the frequency of fluctuations. The nontrivial dependencies of the ratchet velocity on the geometric, frequency, and energy parameters of the system are obtained by numerical implementing the proposed calculation method.

Understanding the Optimal Cooperativity of Human Glucokinase: Kinetic Resonance in Nonequilibrium Conformational Fluctuations.

The cooperativity of a monomeric enzyme arises from dynamic correlation instead of spatial correlation and is a consequence of nonequilibrium conformation fluctuations. We investigate the conformation-modulated kinetics of human glucokinase, a monomeric enzyme with important physiological functions, using a five-state kinetic model. We derive the non-Michealis-Menten (MM) correction term of the activity (i.e., turnover rate), predict its relationship to cooperativity, and reveal the violation of conformational detailed balance. Most importantly, we reproduce and explain the observed resonance effect in human glucokinase (i.e., maximal cooperativity when the conformational fluctuation rate is comparable to the catalytic rate). With the realistic parameters, our theoretical results are in quantitative agreement with the reported measurement by Miller and co-workers. The analysis can be extended to a general chemical network beyond the five-state model, suggesting the generality of kinetic cooperativity and resonance.