Nonequilibrium Chemical Potential Research Articles

Mott Dissociation and Kaon to Pion Ratio in the EPNJL Model

The behaviour of pseudoscalar mesons within the SU(3) PNJL-like models is considered for finite T and $${{\mu }_{B}}$$ . We compare the pole approximation (Breit–Wigner) with the Beth–Uhlenbeck approach. We evaluate the $$K{\text{/}}\pi $$ ratios along the phase transition line in the T– $${{\mu }_{B}}$$ plane with constant and $$T{\text{/}}{{\mu }_{B}}$$ -dependent pion and strange quark chemical potentials. Using the model, we can show that the splitting of kaon and anti-kaon masses appears as a result of introduction of density and this explains the difference in the $${{K}^{ + }}{\text{/}}{{\pi }^{ + }}$$ ratio and $${{K}^{ - }}{\text{/}}{{\pi }^{ - }}$$ ratio at low $$\sqrt {{{s}_{{NN}}}} $$ and their tendency to the same value at high $$\sqrt {{{s}_{{NN}}}} $$ . A sharp “horn” effect in the $${{K}^{ + }}{\text{/}}{{\pi }^{ + }}$$ ratio is explained by the enhanced pion production which can be described by occurrence of a nonequilibrium pion chemical potential of the order of the pion mass. We elucidate that the horn effect is not related to the existence of a critical endpoint in the QCD phase diagram.

Chiral phase transition and kaon-to-pion ratios in the entanglement SU(3) PNJL model

Within the three-flavor PNJL and EPNJL chiral quark models we have obtained pseudoscalar meson properties in quark matter at finite temperature T and baryochemical potential μB. We compare the meson pole (Breit-Wigner) approximation with the Beth-Uhlenbeck (BU) approach that takes into account the continuum of quark-antiquark scattering states when determining the partial densities of pions and kaons. We evaluate the kaon-to-pion ratios along the (pseudo-)critical line in the T − μB plane as a proxy for the chemical freezeout line, whereby the variable x = T∕μB is introduced that corresponds to the conserved entropy per baryon as initial condition for the heavy-ion collision experiments. We present a comparison with the experimental pattern of kaon-to-pion ratios within the BU approach and using x-dependent pion and strange quark potentials. A sharp “horn” effect in the energy dependence K+∕π+ ratio is explained by the enhanced pion production at energies above √sNN=8 GeV, when the system enters the regime of meson dominance. This effect is in line with the enhancement of low-momentum pion spectra that is discussed as a precursor of the pion Bose condensation and entails the occurrence of a nonequilibrium pion chemical potential of the order of the pion mass. We elucidate that the horn effect is not related to the existence of a critical endpoint in the QCD phase diagram.

Pure Spin Current and Magnon Chemical Potential in a Nonequilibrium Magnetic Insulator

Experiments measure, for the first time, two distinct contributions to the spin current in a magnetic insulator as well as the nonequilibrium magnon chemical potential, insight that can inform the development of spin-based technologies.

Nonequilibrium Pion Distribution within the Zubarev Approach

We discuss how the non-equilibrium process of pion production within the Zubarev approach of the non-equilibrium statistical operator leads to a theoretical foundation for the appearance of a non-equilibrium pion chemical potential for the pion distribution function for which there is experimental evidence in experiments at the CERN LHC.

Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviation approach.

We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that the large-deviation function describing the repartition of mass between the two systems is additive, in the sense of being a sum of contributions from each system. We show that this additivity property does not hold for an arbitrary contact dynamics, but is satisfied on condition that a macroscopic detailed balance condition holds at contact, and that the coarse-grained contact dynamics satisfies a factorization property. However, the nonequilibrium chemical potentials of the systems in contact keep track of the contact dynamics, and thus do not obey an equation of state. These nonequilibrium chemical potentials can be related either to the equilibrium chemical potential, or to the nonequilibrium chemical potential of the isolated systems. Results are applied both to an exactly solvable driven lattice gas model and to the Katz-Lebowitz-Spohn model using a numerical procedure to evaluate the chemical potential. The breaking of the additivity property is also illustrated on the exactly solvable model.

Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact.

We discuss the notion of the nonequilibrium chemical potential in gases of non-interacting active particles filling two compartments separated by a potential energy barrier. Different types of active particles are considered: run-and-tumble particles, active Brownian particles, and active Brownian particles with a stochastic reorientation along an external field. After recalling some analytical results for run-and-rumble particles in one dimension, we focus on the two-dimensional case and obtain a perturbative expression of the density profile in the limit of a fast reorientation dynamics, for the three models of active particles mentioned above. Computing the chemical potentials of the nonequilibrium systems in contact from the knowledge of the stationary probability distribution of the whole system-which agrees with a recently proposed general definition of the chemical potential in nonequilibrium systems in contact-we, generically, find that the chemical potential lacks an equation of state in the sense that it depends on the detailed shape of the potential energy barrier separating the compartments and not only on bulk properties, at odds with equilibrium. This situation is reminiscent of the properties of the mechanical pressure in active systems. We also argue that the Maxwell relation is no longer valid and cannot be used to infer the nonequilibrium chemical potential from the knowledge of the mechanical pressure.

Nonequilibrium chemical potential in a two-dimensional electron gas in the quantum-Hall-effect regime

The nonequilibrium state of a two-dimensional electron gas in the quantum-Hall-effect regime is studied in Hall bars equipped with additional inner contacts situated within the bar. The magnetic-field dependence of the voltage drop between different contact pairs are studied at various temperatures. It was found that the voltage between the inner and outer contacts exhibits peaks of significant amplitude in narrow magnetic-field intervals near integer filling factors. Furthermore, the magnetic-field dependence of the voltage in these intervals exhibits a hysteresis, whereas the voltage between the outer contacts remains zero in the entire magnetic-field range. The appearance of the observed voltage peaks and their hysteretic behavior can be explained by an imbalance between the chemical potentials of edge and bulk states, resulting from nonequilibrium charge redistribution between the edge and bulk states when the magnetic field sweeps under conditions of the quantum Hall effect. The results of the study significantly complement the conventional picture of the quantum Hall effect, explicitly indicating the existence of a significant imbalance at the edge of the two-dimensional electron gas: the experimentally observed difference between the electrochemical potentials of the edge and bulk exceeds the distance between Landau levels by tens of times.

Towards a thermodynamics of active matter

Self-propulsion allows living systems to display self-organization and unusual phase behavior. Unlike passive systems in thermal equilibrium, active matter systems are not constrained by conventional thermodynamic laws. A question arises, however, as to what extent, if any, can concepts from classical thermodynamics be applied to nonequilibrium systems like active matter. Here we use the new swim pressure perspective to develop a simple theory for predicting phase separation in active matter. Using purely mechanical arguments we generate a phase diagram with a spinodal and critical point, and define a nonequilibrium chemical potential to interpret the "binodal." We provide a generalization of thermodynamic concepts like the free energy and temperature for nonequilibrium active systems. Our theory agrees with existing simulation data both qualitatively and quantitatively and may provide a framework for understanding and predicting the behavior of nonequilibrium active systems.

Time-dependent Ginzburg–Landau equation of charge-density-waves and numerical simulation of the sliding

Time-dependent Ginzburg–Landau equation (TDGL) for charge-density-wave (CDW) conductors is discussed. At first, we study a purely one-dimensional case, where the current electrodes are attached from the sides. One of the characteristics of our TDGL is that the non-equilibrium chemical potential for right-moving and left-moving electrons are taken into account as dynamical variables. Then the dynamical interaction between the condensate and the quasiparticles is demonstrated in an apparent form. We present some results of the numerical simulation of the sliding of CDW based on our TDGL. Possible extension to quasi-one dimensional (three-dimensional) systems is also discussed.

Statistical theory and applications of lock-in carrierographic image pixel brightness dependence on multi-crystalline Si solar cell efficiency and photovoltage

A solar cell lock-in carrierographic image generation theory based on the concept of non-equilibrium radiation chemical potential was developed. An optoelectronic diode expression was derived linking the emitted radiative recombination photon flux (current density), the solar conversion efficiency, and the external load resistance via the closed- and/or open-circuit photovoltage. The expression was shown to be of a structure similar to the conventional electrical photovoltaic I-V equation, thereby allowing the carrierographic image to be used in a quantitative statistical pixel brightness distribution analysis with outcome being the non-contacting measurement of mean values of these important parameters averaged over the entire illuminated solar cell surface. This is the optoelectronic equivalent of the electrical (contacting) measurement method using an external resistor circuit and the outputs of the solar cell electrode grid, the latter acting as an averaging distribution network over the surface. The statistical theory was confirmed using multi-crystalline Si solar cells.

Thermodynamic theory of phase transitions in driven lattice gases

We formulate an approximate thermodynamic theory of the phase transition in driven lattice gases with attractive nearest-neighbor interactions. We construct the van der Waals equation of state for a driven system where a nonequilibrium chemical potential can be expressed as a function of density and driving field. A Maxwell's construction leads to the phase transition from a homogeneous fluid phase to the coexisting phases of gas and liquid.

Effect of ultrafast diffusion on adsorption, desorption, and reaction processes over heterogeneous surfaces

The effect of ultrafast diffusion is studied on reaction-diffusion processes in heterogeneous media, as encountered in catalysis and field emission microscopy. The reaction-diffusion equations describe adsorption, desorption, and reaction processes for two adspecies, for instance, on a paraboloidal heterogeneous surface in the presence of an external electric field. Using multiscale analysis, we show that the fast adspecies rapidly reaches a quasiequilibrium spatial distribution, characterized by a nonequilibrium chemical potential of the fast adspecies. An ordinary differential equation is derived for the time evolution of the nonequilibrium chemical potential. Numerical simulations are performed under different conditions, which confirm the convergence of the dynamics for finite diffusion toward the ultrafast diffusion limit predicted by our multiscale analysis. The numerical simulations also demonstrate that electric fields may induce important diffusive currents on heterogeneous surfaces under the conditions of field emission microscopy.

Suspension flow modelling in particle migration and microfiltration

We review existing mixture models for shear-induced migration (SIM) in flowing viscous, concentrated particle suspensions via an analysis of the models from the perspective of a two-fluid formulation. Our analysis shows that particle suspensions in strong non-linear shear fields are a prime example of a driven soft matter system. The driving forces for particle migration can be expressed in terms of non-equilibrium osmotic pressure and chemical potential. Using the linear scaling of the effective temperature with the shear stress, we show that the osmotic pressure and shear-induced diffusion coefficients can be written in identical equations. This is similar to the equations for Brownian motion - with the temperature replaced by the effective temperature. As a guiding application we have taken crossflow microfiltration, where the driving is very strong and there is formation of a jammed state, cake layer, coexisting with the fluid state. The question whether the SIM mixture models holds for this aplication is investigated. Another questions is how SIM models can be extended for bidisperse suspensions, which is relevant for microfiltration applications involving particle fractionation. Analysis of existing closures of SIM mixture models from the two-fluid perspective learns us that the theory seems to be extendable towards bidisperse suspensions by means of the effective medium theory.

Non-equilibrium chemical potential and polymer extraction from a porous matrix

The influence of a flow on the transfer of a polymer solution from a porous matrix to a flowing fluid is analysed. Since the flow modifies the free energy of the solution, through stretching and orientation of the macromolecules, the thermodynamic driving force for polymer transport is modified with respect to that of a quiescent fluid. The consequences of this modification for the extraction of a polymer from a porous matrix are explored in detail, and the formal results are explicitly illustrated by means of a specific solution. For the particular example analysed here, of possible interest in oil extraction or in microfluidic problems, the non-equilibrium effects may yield a reduction of the order of 10% of the extraction rate.

Mesoscopic thermodynamics of stationary non-equilibrium states

Thermodynamics for systems at non-equilibrium stationary states have been formulated, based on the assumption of the existence of a local equilibrium in phase space which enables one to interpret the probability density and its conjugated non-equilibrium chemical potential as mesoscopic thermodynamic variables. The probability current is obtained from the entropy production related to the probability diffusion process and leads to the formulation of the Fokker–Planck equation. For the case of a gas of Brownian particles under steady flow in the dilute and concentrated regimes, we derive non-equilibrium equations of state.

Gibbs equation in the nonlinear nonequilibrium thermodynamics of dilute nonviscous gases

This paper deals with the derivation of the Gibbs equation for a nonviscous gas in the presence of heat flux. The analysis aims to shed some light on the physical interpretation of thermodynamic potentials far from equilibrium. Two different definitions for the chemical potential and thermodynamic pressure far from equilibrium are introduced: nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant heat flux q and nonequilibrium chemical potential and nonequilibrium thermodynamic pressure at constant J = V q, where V is the specific volume.

Non-equilibrium chemical potential and stress-induced migration of polymers in tubes

A non-equilibrium chemical potential depending on the viscous pressure tensor is used to describe shear-induced diffusion in polymer solutions flowing along cylindrical tubes. Our results generalize previous ones in three main aspects: a Flory–Huggins expression for the equilibrium contribution to the chemical potential is used instead of the ideal-gas like expression, the full expression for the steady-state compliance of the solution is taken into account instead of only the polymer contribution, and the influence of the solute molecular mass is explicitly considered. As a qualitatively new result of considerable practical interest, it stands the prediction that in some circumstances, a dynamical instability may appear, which accelerates and enhances the separation process.

A thermodynamic model for shear-induced concentration banding and macromolecular separation

We present a simple thermodynamic model for shear-induced concentration banding in polymer solutions, based on a nonequilibrium chemical potential depending on the shear rate. This dependence provides a coupling between diffusion and shear, besides the more classical coupling provided by the divergence of the viscous pressure tensor. When both couplings are taken into account, shear-induced concentration banding appears in a natural way. If the initial homogeneous concentration is higher than a threshold value, shear banding appears for sufficiently high value of the shear rate γ̇; if the initial concentration is lower, the steady-state concentration profile under shear is smooth. The banding profile depends on the polymer molecular mass and therefore it provides a basis for the chromatographic separation of polymers of different molecular mass.

Shear induced polymer migration: analysis of the evolution of concentration profiles

In order to analyze the evolution of the concentration profile experimentally observed by MacDonald and Muller under shear-induced polymer migration in a rotating cone-and-plate device, we use a constitutive equation for the diffusion flux, where the gradient of a generalized non-equilibrium chemical potential appears instead of the concentration gradient. From this model of coupling between diffusion and viscous pressure, together with the mass balance equation, we derive some general features of the concentration profile, the temporal behavior of the polymer concentration near the apex of the cone and some relevant trends of the dynamical process of polymer migration.

Nonequilibrium chemical potential and shear-induced migration of polymers in dilute solutions

We consider the contribution of a nonequilibrium chemical potential depending on the shear rate on shear-induced polymer migration. It is seen that this nonequilibrium contribution strongly enhances, above a threshold of polymer concentration and of shear rate, the migration of the polymer towards the regions with lower stress. This enhancement may explain why the migration rate experimentally observed is much higher than that predicted by constitutive laws where the nonequilibrium effects on the chemical potential are ignored.