Nonequilibrium Stationary State Research Articles

The heavy ion irradiation influence on the thermodynamic parameters of liquids in human body

In this manuscript a theoretical model describing the influence of the heavy ion radiotherapy on the liquid matter in the human body is suggested. Based on the fundamental equations of Bogoliubov chain the effective temperatures in the case of constant particles fluent are found in the context of single component model. An existence of such temperatures allows the use of equilibrium thermodynamics formalism to nonequilibrium stationary state. The obtained results provide the possibility of predicting the liquid matter structural changes in the biological systems in the area influenced by the heavy ion beams.

On the computation of entropy production in stationary social networks

Completing their initial phase of rapid growth, social networks are expected to reach a plateau from where on they are in a statistically stationary state. Such stationary conditions may have different dynamical properties. For example, if each message in a network is followed by a reply in opposite direction, the dynamics is locally balanced. Otherwise, if messages are ignored or forwarded to a different user, one may reach a stationary state with a directed flow of information. To distinguish between the two situations, we propose a quantity called entropy production that was introduced in statistical physics as a measure for non-vanishing probability currents in nonequilibrium stationary states. The proposed quantity closes a gap for characterizing online social networks. As major contribution, we show the relation and difference between entropy production and existing metrics. The comparison shows that computational intensive metrics like centrality can be approximated by entropy production for typical online social networks. To compute the entropy production from real-world measurements, the need for Bayesian inference and the limits of naive estimates for those probability currents are shown. As further contribution, a general scheme is presented to measure the entropy production in small-world networks using Bayesian inference. The scheme is then applied for a specific example of the R mailing list.

The statistical mechanics of the coagulation–diffusion process with a stochastic reset

The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation–diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If, in addition, the input of particles at a fixed given rate is admitted, then a competition between the resetting and the input rates leads to a non-trivial behaviour of the particle-density in the stationary state. From the exact inter-particle probability distribution, a simple physical picture emerges: the reset mainly changes the behaviour at larger distance scales, while at smaller length scales, the non-trivial correlation of the model without a reset dominate.

B-Z化学振荡反应在分析检测中的应用

简单介绍了经典B-Z化学振荡体系，综述了化学振荡的各种行为，规则振荡、混沌、分叉在分析检测中的应用，展望了应用前景。 A brief introduction has been made for classical B-Z oscillation chemical reaction. The application of regular oscillation, chaos, and non-equilibrium stationary state in analytical determination was described. Finally, the prospec- tives of oscillation chemical reaction research and application are prospected.

EMPLOYMENT, PRODUCTION AND CONSUMPTION WITH RANDOM UPDATE: NON-EQUILIBRIUM STATIONARY STATE EQUATIONS

In this work, we investigate the Model of Employment, Production and Consumption, as introduced in a series of papers by I. Wright [1–3] from the perspective of statistical physics, and we focus on the presence of equilibrium. The model itself belongs to the class of multi-agent computational models, which aim to explain macro-economic behavior using explicit micro-economic interactions.<br />Based on the mean-field approximation, we form the Fokker-Plank equation(s) and then formulate conditions forming the stationary solution, which results in a system of non-linear integral-differential equations. This approximation then allows the presence of non-equilibrium stationary states, where the model is a mixed additive-multiplicative model.

Novel symmetry-broken phase in a driven cavity system in the thermodynamic limit

We study non-equilibrium stationary states of a cavity system consisting of many atoms interacting with a quantized cavity field mode, under a driving field in a dissipative environment. We derive a quantum master equation which is suitable for treating systems with a strong driving field and a strong atom–photon interaction. We do this by making use of the fact that the mean-field dynamics are exact in the thermodynamic limit thanks to a uniform coupling between atoms and photons. We find ordered states with symmetry-broken components of the photon field and atomic excitation driven by the external field. The mechanism by which these ordered states arise is discussed from the viewpoint of the quantum interference effect.

Pattern formation and coarsening dynamics in three-dimensional convective mixing in porous media

Geological carbon dioxide (CO2) sequestration entails capturing and injecting CO2 into deep saline aquifers for long-term storage. The injected CO2 partially dissolves in groundwater to form a mixture that is denser than the initial groundwater. The local increase in density triggers a gravitational instability at the boundary layer that further develops into columnar plumes of CO2-rich brine, a process that greatly accelerates solubility trapping of the CO2. Here, we investigate the pattern-formation aspects of convective mixing during geological CO2 sequestration by means of high-resolution three-dimensional simulation. We find that the CO2 concentration field self-organizes as a cellular network structure in the diffusive boundary layer at the top boundary. By studying the statistics of the cellular network, we identify various regimes of finger coarsening over time, the existence of a non-equilibrium stationary state, and a universal scaling of three-dimensional convective mixing.

Nonequilibrium identities of granular vibrating beds

We derive the integral fluctuation theorem around a nonequilibrium stationary state for frictionless and soft core granular particles under an external vibration achieved by a balance between an external vibration and inelastic collisions. We also derive the standard fluctuation theorem and the generalized Green–Kubo formula for this system.

Thermodynamics of quantum-jump-conditioned feedback control

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such systems and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.

Entropy of Non-equilibrium Stationary Measures of Boundary Driven TASEP

We examine the entropy of non-equilibrium stationary states of boundary driven totally asymmetric simple exclusion processes. As a consequence, we obtain that the Gibbs-Shannon entropy of the non equilibrium stationary state converges to the Gibbs-Shannon entropy of the local equilibrium state. Moreover, we prove that its fluctuations are Gaussian, except when the mean displacement of particles produced by the bulk dynamics agrees with the particle flux induced by the density reservoirs in the maximal phase regime.

Kinetic Constraints, Hierarchical Relaxation, and Onset of Glassiness in Strongly Interacting and Dissipative Rydberg Gases

We show that the dynamics of a laser driven Rydberg gas in the limit of strong dephasing is described by a master equation with manifest kinetic constraints. The equilibrium state of the system is uncorrelated but the constraints in the dynamics lead to spatially correlated collective relaxation reminiscent of glasses. We study and quantify the evolution towards equilibrium in one and two dimensions, and analyze how the degree of glassiness and the relaxation time are controlled by the interaction strength between Rydberg atoms. We also find that spontaneous decay of Rydberg excitations leads to an interruption of glassy relaxation that takes the system to a highly correlated nonequilibrium stationary state. The results presented here, which are in principle also applicable to other systems such as polar molecules and atoms with large magnetic dipole moments, show that the collective behavior of cold atomic and molecular ensembles can be similar to that found in soft condensed-matter systems.

Off-equilibrium Langevin dynamics of the discrete nonlinear Schrödinger chain

We introduce suitable Langevin thermostats which are able to control both the temperature and the chemical potential of a one-dimensional lattice of nonlinear Schrödinger oscillators. The resulting nonequilibrium stationary states are then investigated in the limit of low temperatures and large particle densities, where the dynamics can be mapped onto that of a coupled-rotor chain with an external torque. As a result, an effective kinetic definition of temperature can be introduced and compared with the general microcanonical (global) definition.

Dephasing enhanced transport in nonequilibrium strongly correlated quantum systems

A key insight from recent studies is that noise, such as dephasing, can improve the efficiency of quantum transport by suppressing coherent single-particle interference effects. However, it is not yet clear whether dephasing can enhance transport in an interacting many-body system. Here, we address this question by analyzing the transport properties of a boundary driven spinless fermion chain with nearest-neighbor interactions subject to bulk dephasing. The many-body nonequilibrium stationary state is determined using large-scale matrix product simulations of the corresponding quantum master equation. We find dephasing enhanced transport only in the strongly interacting regime, where it is shown to induce incoherent transitions bridging the gap between bound dark states and bands of mobile eigenstates. The generic nature of the transport enhancement is illustrated by a simple toy model, which contains the basic elements required for its emergence. Surprisingly, the effect is significant even in the linear response regime of the full system, and it is predicted to exist for any large and finite chain. The response of the system to dephasing also establishes a signature of an underlying nonequilibrium phase transition between regimes of transport degradation and enhancement. The existence of this transition is shown not to depend on the integrability of the model considered. As a result, dephasing enhanced transport is expected to persist in more realistic nonequilibrium strongly correlated systems.

Two-temperature Langevin dynamics in a parabolic potential

We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the stationary regime the system is described by a nontrivial particle position distribution, P(x,y), which we determine explicitly. We show that this distribution corresponds to a nonequilibrium stationary state, characterized by the presence of space-dependent particle currents which exhibit a nonzero rotor. Theoretical results are confirmed by the numerical simulations.

Langmuir oscillations in a nonextensive electron-positron plasma

The Langmuir oscillations, Landau damping, and growing unstable modes in an electron-positron (EP) plasma are studied by using the Vlasov and Poisson's equations in the context of the Tsallis's nonextensive statistics. Logically, the properties of the Langmuir oscillations in a nonextensive EP plasma are remarkably modified in comparison with that of discussed in the Boltzmann-Gibbs statistics, i.e., the Maxwellian plasmas, because of the system under consideration is essentially a plasma system in a nonequilibrium stationary state with inhomogeneous temperature. It is found that by decreasing the nonextensivity index q which corresponds to a plasma with excess superthermal particles, the phase velocity of the Langmuir waves increases. In particular, depend on the degree of nonextensivity, both of damped and growing oscillations are predicted in a collisionless EP plasma, arise from a resonance phenomena between the wave and the nonthermal particles of the system. Here, the mechanism leads to the unstable modes is established in the context of the nonextensive formalism yet the damping mechanism is the same developed by Landau. Furthermore, our results have the flexibility to reduce to the solutions of an equilibrium Maxwellian EP plasma (extensive limit q→1), in which the Langmuir waves are only the Landau damped modes.

Asymmetric Langevin dynamics for the ferromagnetic spherical model

The present work pursues the investigation of the role of spatial asymmetry and irreversibility on the dynamical properties of spin systems. We consider the ferromagnetic spherical model with asymmetric linear Langevin dynamics. Such an asymmetric dynamics is irreversible, i.e., breaks detailed balance, because the principle of action and reaction is violated. The fluctuation-dissipation theorem therefore no longer holds. The stationary state is however still Gibbsian, i.e., the weights of configurations are given by the Boltzmann factor corresponding to the ferromagnetic Hamiltonian. The model is exactly solvable in any dimension, enabling an analytical evaluation of time-dependent observables. We show the existence of two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite but less than unity and varies continuously with the asymmetry, and a regime of strong violation where the fluctuation-dissipation ratio vanishes asymptotically. This phenomenon was first uncovered in the asymmetric kinetic Ising chain. The present results suggest that this novel kind of dynamical transition in nonequilibrium stationary states might be quite general. We also perform a systematic analysis of several regimes of interest, either stationary or transient, in various dimensions and in the different phases of the model.

The application of oscillating chemical reactions to analytical determinations

Abstract Oscillating chemical reactions, which are far from equilibrium, are extremely sensitive to certain species and may provide new analytical methods using the regular oscillations as well as the non-equilibrium stationary state after system bifurcation. This review of their application to analytical chemistry from 2005 to 2012 includes other appropriate references. Both organic and inorganic analytes are included.

Nonequilibrium stationary state of a current-carrying thermostated system

We find an explicit expression for the long time evolution and stationary speed distribution of N point particles in 2D moving under the action of a weak external field E, and undergoing elastic collisions with either a fixed periodic array of convex scatterers, or with virtual random scatterers. The total kinetic energy of the N-particles is kept fixed by a Gaussian thermostat which induces an interaction between the particles. We show analytically and numerically that for weak fields this distribution is universal, i.e., independent of the position or shape of the obstacles, as far as they form a dispersing billiard with finite horizon, or the nature of the stochastic scattering. Our results are nonperturbative. They exploit the existence of two time scales; the velocity directions become uniformized in times of order unity while the speeds change only on a time scale of O(|E|−2).

ON NONEQUILIBRIUM PHYSICS AND STRING THEORY

In this paper, we review the relation between string theory and nonequilibrium physics based on our previously published work. First, we explain why a theory of quantum gravity and nonequilibrium statistical physics should be related in the first place. Then, we present the necessary background from the recent research in nonequilibrium physics. The review discusses the relationship of string theory and aging phenomena, as well as the connection between AdS/CFT correspondence and the Jarzynski identity. We also discuss the emergent symmetries in fully developed turbulence and the corresponding nonequilibrium stationary states. Finally, we outline a larger picture regarding the relationship between nonperturbative quantum gravity and nonequilibrium statistical physics. This relationship can be understood as a natural generalization of the well-known Wilsonian relation between local quantum field theory and equilibrium statistical physics of critical phenomena. According to this picture, the AdS/CFT duality is just an example of a more general connection between nonperturbative quantum gravity and nonequilibrium physics. In the appendix of this review, we discuss a new kind of complementarity between thermodynamics and statistical physics which should be important in the context of black hole complementarity.

Clausius Inequality and Optimality of Quasistatic Transformations for Nonequilibrium Stationary States

Nonequilibrium stationary states of thermodynamic systems dissipate a positive amount of energy per unit of time. If we consider transformations of such states that are realized by letting the driving depend on time, the amount of energy dissipated in an unbounded time window then becomes infinite. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work performed along any given transformation. We then show that the renormalized work satisfies a Clausius inequality and prove that equality is achieved for very slow transformations, that is, in the quasistatic limit. We finally connect the renormalized work to the quasipotential of the macroscopic fluctuation theory, which gives the probability of fluctuations in the stationary nonequilibrium ensemble.