Showing papers on "Non-equilibrium thermodynamics published in 2013"
Book•
01 Sep 2013
TL;DR: In this article, the authors discuss the properties of high-temperature gas dynamics, including the effects of high temperature on the dynamics of Viscous Flow and Vibrational Nonequilibrium Flows.
Abstract: Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.
1,960 citations
TL;DR: In condensed matter, strong interactions alter chemical activities and create variations that can dramatically affect the reaction rate as mentioned in this paper, and the extreme case is that of a reaction coupled to a phase transformation whose kinetics must depend not only on the order parameter but also on its gradients at phase boundaries.
Abstract: Advances in the fields of catalysis and electrochemical energy conversion often involve nanoparticles, which can have kinetics surprisingly different from the bulk material. Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create variations that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend not only on the order parameter but also on its gradients at phase boundaries. Reaction-driven phase transformations are common in electrochemistry, when charge transfer is accompanied by ion intercalation or deposition in a solid phase. Examples abound in Li-ion, metal–air, and lead–acid batteries, as well as metal electrodeposition–dissolution. Despite complex thermodynamics, however, the standard kinetic model is the Butler–Volmer equation, based on a dilute s...
497 citations
TL;DR: In this article, complete Boltzmann collision integrals were applied to describe the transient electron distribution due to excitation, thermalization, and relaxation, and the electron-phonon coupling strength was analyzed under nonequilibrium conditions.
Abstract: When an ultrashort laser pulse irradiates a metal, energy is absorbed by the electron system which is driven out of thermal equilibrium on a femtosecond time scale. Due to electron-electron collisions, a new thermodynamical equilibrium state within the electron system is established in a characteristic time, the so-called thermalization time. The absorbed energy of the electrons will be further transferred to the phononic system. The thermalization time as well as the electron-phonon coupling strength both strongly depend on the material properties and the excitation type. Furthermore, a nonthermalized electron gas couples differently to the phononic system as a thermalized one. In order to follow the relevant microscopic dynamics without the need to assume thermalized electrons, we apply complete Boltzmann collision integrals to describe the transient electron distribution due to excitation, thermalization, and relaxation. We implement the density of states of real materials in our approach. As a result of our simulations, we extract the electron thermalization time and the electron-phonon coupling under nonequilibrium conditions. Examples are given for aluminum, gold, and nickel.
240 citations
20 Feb 2013
TL;DR: In this paper, a pedagogical overview of fluctuation relations and the foundations of statistical thermodynamics is presented, along with a deterministic approach and numerical demonstration for measuring out of equilibrium fluctuations.
Abstract: Part I: Fluctuation relations Fluctuation relations: A pedagogical overview Fluctuation Relations and the foundations of statistical thermodynamics: A deterministic approach and numerical demonstration Fluctuation relations in small systems: Exact results from the deterministic approach Measuring out of equilibrium fluctuations Recent progress in fluctuation theorems and free energy recovery Information thermodynamics: Maxwell's demon in nonequilibrium dynamics Time-reversal symmetry relations for currents in nonequilibrium stochastic and quantum systems Anomalous fluctuation relations Part II: Beyond fluctuation relations Out-of-equilibrium generalized fluctuation-disspation relations Anomalous thermal transport in nanostructures Large deviation approach to nonequilibrium systems Lyapunov modes in extended systems Study of single molecule dynamics in mesoporous systems, glasses and living cells
172 citations
TL;DR: A simple and solvable model of a device that-like the "neat-fingered being" in Maxwell's famous thought experiment-transfers energy from a cold system to a hot system by rectifying thermal fluctuations is described.
Abstract: We describe a simple and solvable model of a device that---like the ``neat-fingered being'' in Maxwell's famous thought experiment---transfers energy from a cold system to a hot system by rectifying thermal fluctuations. In order to accomplish this task, our device requires a memory register to which it can write information: the increase in the Shannon entropy of the memory compensates the decrease in the thermodynamic entropy arising from the flow of heat against a thermal gradient. We construct the nonequilibrium phase diagram for this device, and find that it can alternatively act as an eraser of information. We discuss our model in the context of the second law of thermodynamics.
149 citations
TL;DR: In this paper, the first-passage time problems for a diusive particle with stochastic resetting with a non-vanishing resetting rate were studied and the optimal search time was compared quantitatively with that of an eective equilibrium Langevin process with the same stationary distribution.
Abstract: We study rst-passage time problems for a diusive particle with stochastic resetting with a nite rate r. The optimal search time is compared quantitatively with that of an eective equilibrium Langevin process with the same stationary distribution. It is shown that the intermittent, nonequilibrium strategy with non-vanishing resetting rate is more ecient than the equilibrium dynamics. Our results are extended to multiparticle systems where a team of independent searchers, initially uniformly distributed with a given density, looks for a single immobile target. Both the average and the typical survival probability of the target are smaller in the case of nonequilibrium dynamics.
135 citations
TL;DR: In this paper, the authors derived a third-order hydrodynamic evolution equation for the shear stress tensor from kinetic theory and showed that the results obtained using the thirdorder viscous equations derived here provide a very good approximation to the exact solution of the Boltzmann equation in a relaxation time approximation.
Abstract: We present the derivation of a novel third-order hydrodynamic evolution equation for the shear stress tensor from kinetic theory. The Boltzmann equation with a relaxation time approximation for the collision term is solved iteratively using a Chapman-Enskog-like expansion to obtain the nonequilibrium phase-space distribution function. Subsequently, the evolution equation for the shear stress tensor is derived from its kinetic definition up to third order in gradients. We quantify the significance of the new derivation within a one-dimensional scaling expansion and demonstrate that the results obtained using the third-order viscous equations derived here provides a very good approximation to the exact solution of the Boltzmann equation in a relaxation time approximation. We also show that the time evolution of pressure anisotropy obtained using our equations is in better agreement with transport results than that obtained with an existing third-order calculation based on the second law of thermodynamics.
118 citations
TL;DR: The nonequilibrium screening potential of a generic mesoscopic system is determined and it is found that its response is dictated by particle and entropic injectivities which describe the charge and entropy transfer during transport.
Abstract: We investigate nonlinear transport properties of quantum conductors in response to both electrical and thermal driving forces. Within the scattering approach, we determine the nonequilibrium screening potential of a generic mesoscopic system and find that its response is dictated by particle and entropic injectivities which describe the charge and entropy transfer during transport. We illustrate our model analyzing the voltage and thermal rectification of a resonant tunneling barrier. Importantly, we discuss interaction induced contributions to the thermopower in the presence of large temperature differences.
114 citations
TL;DR: In this article, the quantum analogues for driven open quantum systems describable by quantum jump trajectories by applying a quantum stochastic thermodynamics were derived based on a quantum formulation of the local detailed balance condition.
Abstract: For classical nonequilibrium systems, the separation of the total entropy production into the adiabatic and nonadiabatic contributions is useful for understanding irreversibility in nonequilibrium thermodynamics. In this paper, we formulate quantum analogues for driven open quantum systems describable by quantum jump trajectories by applying a quantum stochastic thermodynamics. Our main conclusions are based on a quantum formulation of the local detailed balance condition.
105 citations
TL;DR: In this paper, the authors consider two quantum Ising chains initially prepared at thermal equilibrium but with different temperatures and coupled at a given time through one of their end points, and show that the heat transport is ballistic.
Abstract: We consider two quantum Ising chains initially prepared at thermal equilibrium but with different temperatures and coupled at a given time through one of their end points. In the long-time limit the system reaches a nonequilibrium steady state. We discuss properties of this nonequilibrium steady state and characterize the convergence to the steady regime. We compute the mean energy flux through the chain and show that the heat transport is ballistic. We derive also the large-deviation function for the quantum and thermal fluctuations of this energy transfer.
98 citations
TL;DR: In this paper, the authors investigated nonlinear heat properties in mesoscopic conductors using a scattering theory of transport, based on a leading-order expansion in both the electrical and thermal driving forces.
Abstract: We investigate nonlinear heat properties in mesoscopic conductors using a scattering theory of transport. Our approach is based on a leading-order expansion in both the electrical and thermal driving forces. Beyond linear response, the transport coefficients are functions of the nonequilibrium screening potential that builds up in the system due to interactions. Within a mean-field approximation, we self-consistently calculate the heat rectification properties of a quantum dot attached to two terminals. We discuss nonlinear contributions to the Peltier effect and find departures from the Wiedemann-Franz law in the nonlinear regime of transport.
TL;DR: In this paper, the authors revisited the description of permeability and diffusivity in glassy polymers by considering the diffusion coefficient as the product of a kinetic factor, mobility, and a thermodynamic factor associated to the concentration dependence of the chemical potential of the diffusing species.
11 Feb 2013
TL;DR: The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing as discussed by the authors.
Abstract: The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A similar approach has been followed more recently for nonequilibrium systems, especially in the context of interacting particle systems. We review here the basis of this approach, emphasizing the similarities and differences that exist between the application of large deviation theory for studying equilibrium systems on the one hand and nonequilibrium systems on the other. Of particular importance are the notions of macroscopic, hydrodynamic, and long-time limits, which are analogues of the equilibrium thermodynamic limit, and the notion of statistical ensembles which can be generalized to nonequilibrium systems. For the purpose of illustrating our discussion, we focus on applications to Markov processes, in particular to simple random walks.
TL;DR: In this article, the authors show how the glass transition can be interpreted quantitatively in terms of an East-model picture of localized excitations (or soft spots) in which molecules can move with a specific direction, and from which excitations with the same directionality of motion can appear or disappear in adjacent regions.
Abstract: The glass transition refers to the nonequilibrium process by which an equilibrium liquid is transformed to a nonequilibrium disordered solid, or vice versa. Associated response functions, such as heat capacities, are markedly different on cooling than on heating, and the response to melting a glass depends markedly on the cooling protocol by which the glass was formed. This paper shows how this irreversible behavior can be interpreted quantitatively in terms of an East-model picture of localized excitations (or soft spots) in which molecules can move with a specific direction, and from which excitations with the same directionality of motion can appear or disappear in adjacent regions. As a result of these facilitated dynamics, excitations become correlated in a hierarchical fashion. These correlations are manifested in the dynamic heterogeneity of the supercooled liquid phase. Although equilibrium thermodynamics is virtually featureless, a nonequilibrium glass phase emerges when the model is driven out of equilibrium with a finite cooling rate. The correlation length of this emergent phase is large and increases with decreasing cooling rate. A spatially and temporally resolved fictive temperature encodes memory of its preparation. Parameters characterizing the model can be determined from reversible transport data, and with these parameters, predictions of the model agree well with irreversible differential scanning calorimetry.
TL;DR: In this paper, the dispersion relation for sound in rarefied polyatomic gases (hydrogen, deuterium and hydrogen deuteride gases) is studied based on the recently developed theory of extended thermodynamics (ET) of dense gases.
Abstract: We study the dispersion relation for sound in rarefied polyatomic gases (hydrogen, deuterium and hydrogen deuteride gases) basing on the recently developed theory of extended thermodynamics (ET) of dense gases. We compare the relation with those obtained in experiments and by the classical Navier–Stokes Fourier (NSF) theory. The applicable frequency range of the ET theory is proved to be much wider than that of the NSF theory. We evaluate the values of the bulk viscosity and the relaxation times involved in nonequilibrium processes. The relaxation time related to the dynamic pressure has a possibility to become much larger than the other relaxation times related to the shear stress and the heat flux.
TL;DR: In this article, a thermodynamically consistent phase field theory for multivariant martensitic transformations is developed with the main focus on introducing correct interface stresses (tension), where the interface tension is introduced with the help of some geometric nonlinearities, even when strains are infinitesimal.
TL;DR: In this article, an analytic expression for the cumulant generating function, accurate up to second order in the electron-phonon coupling and valid for finite voltages and temperatures, is obtained in the extended wide-band limit.
Abstract: We study the full-counting statistics of charges transmitted through a single-level quantum dot weakly coupled to a local Einstein phonon which causes fluctuations in the dot energy. An analytic expression for the cumulant generating function, accurate up to second order in the electron-phonon coupling and valid for finite voltages and temperatures, is obtained in the extended wide-band limit. The result accounts for nonequilibrium phonon distributions induced by the source-drain bias voltage, and concomitantly satisfies the fluctuation theorem. Extending the counting field to the complex plane, we investigate the locations of possible singularities of the cumulant generating function, and exploit them to identify regimes in which the electron transfer is affected differently by the coupling to the phonons. Within a large-deviation analysis, we find a kink in the probability distribution, analogous to a first-order phase transition in thermodynamics, which would be a unique hallmark of the electron-phonon correlations. This kink reflects the fact that although inelastic scattering by the phonons once the voltage exceeds their frequency can scatter electrons opposite to the bias, this will never generate current flowing against the bias at zero temperature, in accordance with the fluctuation theorem. DOI: 10.1103/PhysRevB.87.115407
TL;DR: In this article, the authors investigated the physics of the quantum $O(N) model in the infinite-N$ limit and showed that the model does not lead to equilibration on account of an infinite number of conserved quantities.
Abstract: The quantum $O(N)$ model in the infinite-$N$ limit is a paradigm for symmetry breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of $N$ in varying spatial dimensions ($dg1$). Here, we investigate the physics of this model out of equilibrium, specifically its response to global quenches starting in the disordered phase. If the model were to exhibit equilibration, the late-time state could be inferred from the finite-temperature phase diagram. In the infinite-$N$ limit, we show that not only does the model not lead to equilibration on account of an infinite number of conserved quantities, it also does not relax to a generalized Gibbs ensemble (GGE) consistent with these conserved quantities. Instead, an infinite number of new conservation laws emerge at late times and the system relaxes to an emergent GGE consistent with these. Nevertheless, we still find that the late-time states following quenches bear strong signatures of the equilibrium phase diagram. Notably, we find that the model exhibits coarsening to a nonequilibrium critical state only in dimensions $dg2$, that is, if the equilibrium phase diagram contains an ordered phase at nonzero temperatures.
TL;DR: These studies extend the understanding of CCFs from thermal equilibrium to nonequilibrium processes, which are relevant to current experiments, and show the emergence of significant effects near the critical point.
Abstract: Colloids immersed in a critical binary liquid mixture are subject to critical Casimir forces (CCFs) because they confine its concentration fluctuations and influence the latter via effective surface fields. To date, CCFs have been primarily studied in thermodynamic equilibrium. However, due to the critical slowing down, the order parameter around a particle can easily be perturbed by any motion of the colloid or by solvent flow. This leads to significant but largely unexplored changes in the CCF. Here we study the drag force on a single colloidal particle moving in a near-critical fluid mixture and the relative motion of two colloids due to the CCF acting on them. In order to account for the kinetic couplings among the order parameter field, the solvent velocity field, and the particle motion, we use a fluid particle dynamics method. These studies extend the understanding of CCFs from thermal equilibrium to nonequilibrium processes, which are relevant to current experiments, and show the emergence of significant effects near the critical point.
TL;DR: In this paper, the second law of classical thermodynamics in terms of the entropy principle was presented, and an empirically accessible axiomatic derivati cation for the second Law was provided.
Abstract: In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivati...
TL;DR: In this paper, the authors investigated the thermodynamics at the apparent horizon of the FRW universe in f(R, T) theory in the nonequilibrium description and established the conditions for the generalized second law of thermodynamics to be preserved with the constraints of positive temperature and attractive gravity.
Abstract: We investigate the thermodynamics at the apparent horizon of the FRW universe in f(R, T) theory in the nonequilibrium description. The laws of thermodynamics are discussed for two particular models of the f(R, T) theory. The first law of thermodynamics is expressed in the form of the Clausius relation \(T_h d\hat S_h = \delta Q\), where δQ is the energy flux across the horizon and \(d\hat S\) is the entropy production term. Furthermore, the conditions for the generalized second law of thermodynamics to be preserved are established with the constraints of positive temperature and attractive gravity. We illustrate our results for some concrete models in this theory.
TL;DR: In this paper, the Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice was measured in equilibrium and non-equilibrium situations.
Abstract: We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi–Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.
TL;DR: In this article, a molecular dynamics study of the micro-spallation of lead (Pb) is presented, which corresponds to damage and liquid fragment ejection following the reflection of a strong shock wave on the free surface of the target.
Abstract: We present a molecular dynamics (MD) study of the micro-spallation of lead (Pb), which corresponds to damage and liquid fragment ejection following the reflection of a strong shock wave on the free surface of the target. First, the Hugoniot and melting curves of Pb are derived by equilibrium MD simulations, and the potential function is validated by comparing these curves with experimental results. Then nonequilibrium MD simulations are conducted to study the dynamical processes of micro-spallation. Damage and ejection processes are analyzed by a binning analysis and direct observations of atom configurations. Comparisons with classical spallation simulations or experiments are made where necessary. It is found that damages in classical spallation and micro-spallation are both dominated by cavitation, i.e. nucleation and the growth and coalescence of voids. The main difference in the cavitation process of classical and micro-spallation lies in the amount and spatial distribution of void nucleation sites. Different properties in dynamical stress evolutions between micro-spallation and classical spallation are also discussed. In addition, the properties of the surface micro-spall are found to be different from those of interior micro-spall particles in some shock intensity regimes. Factors that cause such differences are studied by analyzing in detail the thermodynamics paths of different parts of the shocked target.
TL;DR: In this article, the authors study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture.
Abstract: Understanding the physics of nonequilibrium systems remains as one of the major challenges of theoretical physics. This problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics and associated structures. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new general methods have appeared to investigate fluctuating behavior that are changing radically our understanding of nonequilibrium physics: a powerful macroscopic fluctuation theory (MFT) and a set of advanced computational techniques to measure rare events. In this work we study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture. Our quest will bring us from (1) the confirmation of an additivity conjecture in one and two dimensions, which considerably simplifies the MFT complex variational problem to compute the thermodynamics of currents, to (2) the discovery of novel isometric fluctuation relations, which opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations, and to (3) the observation of coherent structures in fluctuations, which appear via dynamic phase transitions involving a spontaneous symmetry breaking event at the fluctuating level. The clear-cut observation, measurement and characterization of these unexpected phenomena, well described by MFT, strongly support this theoretical scheme as the natural theory to understand the thermodynamics of currents in nonequilibrium diffusive media, opening new avenues of research in nonequilibrium physics.
TL;DR: In this paper, the degeneracy in bulk viscous cosmologies is discussed and the possibility that phantom dark energy cosmology could be caused by the existence of nonequilibrium pressure in any one of the cosmic components.
Abstract: In a homogeneous and isotropic universe bulk viscosity is the unique viscous effect that is capable of modifying the background dynamics. Effects like shear viscosity or heat conduction can only change the evolution of the perturbations. The existence of a bulk viscous pressure in a fluid-which in order to obey the second law of thermodynamics must be negative-reduces its effective pressure. We discuss the degeneracy in bulk viscous cosmologies and address the possibility that phantom dark energy cosmology could be caused by the existence of nonequilibrium pressure in any one of the cosmic components. We establish the conditions under which either viscous matter or radiation cosmologies can be mapped into the phantom dark energy scenario with constraints from multiple observational data sets.
TL;DR: It is demonstrated that the same physical properties which are responsible for the superdiffusivity in nonequilibrium systems also determine the non-Gaussian parameter in equilibrium systems.
Abstract: We perform nonequilibrium dynamics simulations of a binary Lennard-Jones mixture in which an external force is applied on a single tagged particle. For the diffusive properties of this particle parallel to the force, superdiffusive behavior at intermediate times as well as giant long-time diffusivity is observed. A quantitative description of this nontrivial behavior is given by a continuous time random walk analysis of the system in configuration space. We further demonstrate that the same physical properties which are responsible for the superdiffusivity in nonequilibrium systems also determine the non-Gaussian parameter in equilibrium systems.
TL;DR: In this paper, the authors consider the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies, and present necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves.
Abstract: We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degenerate). In this case, the only free operations are those that add noise to the system (or implement a reversible evolution) and the only nonequilibrium states are states of informational nonequilibrium, that is, states that deviate from the maximally mixed state. The degree of this deviation we call the state's nonuniformity; it is the resource of interest here, the fuel that is consumed, for instance, in an erasure operation. We consider the different types of state conversion: exact and approximate, single-shot and asymptotic, catalytic and noncatalytic. In each case, we present the necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves. We also review the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies. Quantum state conversion problems in this resource theory can be shown to be always reducible to their classical counterparts, so that there are no inherently quantum-mechanical features arising in such problems. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible.
TL;DR: In this article, a simple and general approach to formulate the lattice BGK model for high-speed compressible flows is presented, which consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) feq and a discrete velocity model with flexible velocity size.
Abstract: We present a simple and general approach to formulate the lattice BGK model for high-speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) feq and a discrete velocity model with flexible velocity size. The DEDF is obtained by feq = C−1M, where M is a set of moments of the Maxwellian distribution function, and C is the matrix connecting the DEDF and the moments. The numerical components of C are determined by the discrete velocity model. The calculation of C−1 is based on the analytic solution which is a function of the parameter controlling the sizes of discrete velocity. The choice of the discrete velocity model has a high flexibility. The specific-heat ratio of the system can be flexible. The approach works for the one-, two- and three-dimensional model constructions. As an example, we compose a new lattice BGK kinetic model which works not only for recovering the Navier-Stokes equations in the continuum limit but also for measuring the departure of the system from its thermodynamic equilibrium. Via adjusting the sizes of the discrete velocities, the stably simulated Mach number can be significantly increased up to 30 or even higher. The model is verified and validated by well-known benchmark tests. Some macroscopic behaviors of the system due to the deviation from thermodynamic equilibrium around the shock wave interfaces are shown.
TL;DR: A lower bound on the entropy production is derived in terms of the Bures angle between the nonequilibrium and the corresponding equilibrium state of the system, which defines a thermodynamic length valid arbitrarily far from equilibrium.
Abstract: We consider a closed quantum system initially at thermal equilibrium and driven by arbitrary external parameters. We derive a lower bound on the entropy production which we express in terms of the Bures angle between the nonequilibrium and the corresponding equilibrium state of the system. The Bures angle is an angle between mixed quantum states and defines a thermodynamic length valid arbitrarily far from equilibrium. As an illustration, we treat the case of a time-dependent harmonic oscillator for which we obtain analytic expressions for generic driving protocols.
TL;DR: Extended applications of an established theoretical and computational machinery suitable for the study of the dynamics of CO2+CO2 collisions are presented, focusing on vibrational energy exchange, considered over a wide range of energies and rotational temperatures.
Abstract: We present extended applications of an established theoretical and computational machinery suitable for the study of the dynamics of CO2+CO2 collisions, focusing on vibrational energy exchange, considered over a wide range of energies and rotational temperatures. Calculations are based on quasi-classical trajectories on a potential energy function (a critical component of dynamics simulations), tailored to accurately describe the intermolecular interactions, modeled by the recently proposed bond-bond semiempirical formulation that allows the colliding molecules to be stretchable, rather than frozen at their equilibrium geometry. In a previous work, the same potential energy surface has been used to show that modifications in the geometry (and in physical properties such as polarizability and charge distribution) of the colliding partners affect the intermolecular interaction and determine the features of the energy exchange, to a large extent driven by long-range forces. As initial partitioning of the energy among the molecular degrees of freedom, we consider the excitation of the vibrational bending mode, assuming an initial rotational distribution and a rotational temperature. The role of the vibrational angular momentum is also carefully assessed. Results are obtained by portable implementations of this approach in a Grid-computing framework and on high performance platforms. Cross sections are basic ingredients to obtain rate constants of use in advanced state-to-state kinetic models, under equilibrium or nonequilibrium conditions, and this approach is suitable for gas dynamics applications to plasmas and modeling of hypersonic flows.