Depletion forces in nonequilibrium

The concept of effective depletion forces between two fixed big colloidal particles in a bath of small particles is generalized to a nonequilibrium situation where the bath of small Brownian particles is flowing around the big particles with a prescribed velocity. In striking contrast to the equilibrium case, the nonequilibrium forces violate Newton's third law; they are nonconservative and strongly anisotropic, featuring both strong attractive and repulsive domains.     

Effective interactions between colloidal particles suspended in a bath of swimming cells

The dynamics of passive colloidal tracers in a bath of self-propelled particles is receiving a lot of attention in the context of nonequilibrium statistical mechanics. Here we demonstrate that active baths are also capable of mediating effective interactions between suspended bodies. In particular we observe that a bath of swimming bacteria gives rise to a short range attraction similar to depletion forces in equilibrium colloidal suspensions. Using numerical simulations and experiments we show how the features of this interaction arise from the combination of nonequilibrium dynamics (peculiar of bacterial baths) and excluded volume effects.     

Osmotic propulsion: the osmotic motor

A model for self-propulsion of a colloidal particle--the osmotic motor--immersed in a dispersion of "bath" particles is presented. The nonequilibrium concentration of bath particles induced by a surface chemical reaction creates an osmotic pressure imbalance on the motor causing it to move. The ratio of the speed of reaction to that of diffusion governs the bath particle distribution which is employed to calculate the driving force on the motor, and from which the self-induced osmotic velocity is determined. For slow reactions, the self-propulsion is proportional to the reaction velocity. When surface reaction dominates over diffusion the osmotic velocity cannot exceed the diffusive speed of the bath particles. Implications of these features for different bath particle volume fractions and motor sizes are discussed. Theoretical predictions are compared with Brownian dynamics simulations.     

Disordered Markovian Brownian ratchets

A model of a Brownian ratchet coupled to a heat bath and driven by a nonequilibrium Poisson white noise is discussed. The formula describing a generated current in terms of the statistical properties of a possible irregular or random potential is derived within the small nonequilibrium noise approximation and illustrated by a few concrete examples. The perturbation technique for Hilbert space operators is used as a mathematical tool.     

Memory effects in the two-level model for glasses

We study an ensemble of two-level systems interacting with a thermal bath. This is a well-known model for glasses. The origin of memory effects in this model is a quasistationary but nonequilibrium state of a single two-level system, which is realized due to a finite-rate cooling and slow thermally activated relaxation. We show that single-particle memory effects, such as negativity of the specific heat under reheating, vanish for a sufficiently disordered ensemble. In contrast, a disordered ensemble displays a collective memory effect [similar to the Kovacs effect], where nonequilibrium features of the ensemble are monitored via a macroscopic observable. An experimental realization of the effect can be used to further assess the consistency of the model.     

Thermal and reactive nonequilibrium of magnetoactive plasma flows

Based on multifluid equations derived from the Boltzman equation under inclusion of ionization and recombination reactions, the following convective processes in magnetoactive plasma flows transverse to homogeneous magnetic fields are investigated:The build-up of the nonuniform plasma state, the intercomponent thermal nonequilibrium and the reactive nonequilibrium in dependence of the flow coordinate. Due to the complexity of the problem, a numerical approach is used, parallel to which an approximate analytical theory is developed.     

Quantum Thermodynamic Uncertainty Relations,Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities

Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong et al., Entropy 2022, 24, 870], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.     

Bose-Einstein condensation quantum kinetics for a gas of interacting excitons

A quantum kinetics of the Bose-Einstein condensation in the self-consistent (s.c.) Hartree-Fock-Bogoliubov (HFB) model of the interacting Bose gas is formulated and numerically solved for the example of excitons scattering with a thermal bath of acoustic phonons. The theory describes the condensation in real time starting from a nonequilibrium initial state towards the equilibrium HFB solution. The s.c. changes of the spectrum are automatically incorporated in the scattering terms.     

New developments in the Nonequilibrium Dynamics of spin glasses

We present an overview of recent developments in the nonequilibrium dynamics of spin glasses. The prevailing theoretical pictures are described and discussed in light of numerical results and experimental observations. We focus on aging phenomena like waiting-time-dependent length scales, scaling of two-time quantities, more complex temperature protocols during aging, and the violation of the fluctuation–dissipation theorem. Finally, aging in quantum spin glass models coupled to a dissipative bath is discussed.     

Phase transitions in a driven lattice gas in two planes

We report on a Monte Carlo study of ordering in a nonequilibrium system. The system is a lattice gas that comprises two equal, parallel square lattices with stochastic particle-conserving irreversible dynamics. The particles are driven along a principal direction under the competition of the heat bath and a large, constant external electric field. There is attraction only between particles on nearest-neighbor sites within the same lattice. Particles may jump from one plane to the other; therefore, density fluctuations have an extra mechanism to decay and build up. It helps to obtain the steady-state accurately. Spatial correlations decay with distance according to a power law at high enough temperature, as for the ordinary two-dimensional case. We find two kinds of nonequilibrium phase transitions. The first one has a critical point for half occupation of the lattice, and seems to be related to the anisotropic phase transition reported before for the plane. This transition becomes discontinuous for low enough density. The difference of density between the planes changes discontinuously for any density at a lower temperature. This seems to correspond to a phase transition that does not have a counterpart in equilibrium nor in the two-dimensional nonequilibrium case.     

Ergodicity and Energy Distributions for Some Boundary Driven Integrable Hamiltonian Chains

We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.     

Probing the fluctuation-dissipation theorem in a Perrin-like experiment

In this Letter, we present a new experimental approach to investigate the effective temperature concept as a generalization of the fluctuation-dissipation theorem (FDT) for nonequilibrium systems. Simultaneous measurements of diffusion coefficient and sedimentation velocity of heavy colloids, embedded in a Laponite clay suspension, are performed with a fluorescence-recovery-based setup. This nonperturbative dual measurement, performed at a single time in a single sample, allows for a direct application of the FDT to the tracer velocity observable. It thus provides a well-defined derivation of the effective temperature in this ageing colloidal gel. For a wide range of concentrations and ageing times, we report no violation of the FDT, with effective temperature agreeing with bath temperature. This result is consistent with recent theoretical predictions on the coupling between the velocity observable and nonequilibrium gels dynamics.     

Dynamic stimulation of quantum coherence in systems of lattice bosons

Thermal fluctuations tend to destroy long-range phase correlations. Consequently, bosons in a lattice will undergo a transition from a phase-coherent superfluid as the temperature rises. Contrary to common intuition, however, we show that nonequilibrium driving can be used to reverse this thermal decoherence. This is possible because the energy distribution at equilibrium is rarely optimal for the manifestation of a given quantum property. We demonstrate this in the Bose-Hubbard model by calculating the nonequilibrium spatial correlation function with periodic driving. We show that the nonequilibrium phase boundary between coherent and incoherent states at finite bath temperatures can be made qualitatively identical to the familiar zero-temperature phase diagram, and we discuss the experimental manifestation of this phenomenon in cold atoms.     

Expression for the stationary distribution in nonequilibrium steady states

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths. Starting from the detailed fluctuation theorem, we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate eta is proportional to exp[Phi(eta)] where Phi(eta)=-[under summation operator]kbeta_{k}E_{k}(eta) is the excess entropy change. Here, E_{k}(eta) is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the kth heat bath whose inverse temperature is beta_{k}. This result can be easily extended to steady states maintained with other sources, e.g., particle current driven by an external force. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.     

Fractal dimension of steady nonequilibrium flows

The Kaplan-Yorke information dimension of phase-space attractors for two kinds of steady nonequilibrium many-body flows is evaluated. In both cases a set of Newtonian particles is considered which interacts with boundary particles. Time-averaged boundary temperatures are imposed by Nose-Hoover thermostat forces. For both kinds of nonequilibrium systems, it is demonstrated numerically that external isothermal boundaries can drive the otherwise purely Newtonian flow onto a multifractal attractor with a phase-space information dimension significantly less than that of the corresponding equilibrium flow. Thus the Gibbs' entropy of such nonequilibrium flows can diverge.     

Non-Markovian Two-Time Correlation Dynamics and Nonergodicity

The two-time correlation functions of the coordinate and velocity of a non-Markovian harmonic particle are derived analytically. They are decomposed into the components of differences between the initial variances and the equilibrium of the particle; in particular, the dependence of a random force on the initial preparation of the system is included. Using those expressions, we simultaneously investigate nonstationary, nonergodic, and nonequilibrium features of a forced system. It is demonstrated that the result of combining the oscillating relaxation and the initial preparation-dependent noise leads to breakdown of both ergodicity and equilibration of a forced system. The finite-size effect of a coupled-oscillator-chain heat bath is also discussed.     

Use and Abuse of Entropy in Biology: A Case for Caliber

Here, I discuss entropy and its use as a tool in fields of biology such as bioenergetics, ecology, and evolutionary biology. Statistical entropy concepts including Shannon’s diversity, configurational entropy, and informational entropy are discussed in connection to their use in describing the diversity, heterogeneity, and spatial patterning of biological systems. The use of entropy as a measure of biological complexity is also discussed, and I explore the extension of thermodynamic entropy principles to open, nonequilibrium systems operating in finite time. I conclude with suggestions for use of caliber, a metric similar to entropy but for time-dependent trajectories rather than static distributions, and propose the complementary notion of path information.     

Nonequilibrium steady state in open quantum systems: Influence action,stochastic equation and power balance

The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of classical harmonic oscillators connected at each end to a heat bath, and for classical anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculating the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics.