Journal of Statistical Physics最新文献

Approach of mesoscopic state variables to time independent equilibrium sates (zero law of thermodynamics) gives birth to the classical equilibrium thermodynamics. Approach of fluxes and forces to fixed points (equilibrium fluxes and forces) that drive reduced mesoscopic dynamics gives birth to the rate thermodynamics that is applicable to driven systems. We formulate the rate thermodynamics and dynamics, investigate its relation to the classical thermodynamics, to extensions involving more details, to the hierarchy reformulations of dynamical theories, and to the Onsager variational principle. We also compare thermodynamic and dynamic critical behavior observed in closed and open systems. Dynamics and thermodynamics of the van der Waals gas provides an illustration.

We consider the symmetric Markov random flight, also called the persistent random walk, performed by a particle that moves at constant finite speed in the Euclidean space (mathbb {R}^m, ; mge 2,) and changes its direction at Poisson-distributed time instants by taking it at random according to the uniform distribution on the surface of the unit ((m-1))-dimensional sphere. Such stochastic motion has become a very popular object of modern statistical physics because it can serve as an appropriate model for describing the isotropic finite-velocity transport in multidimensional Euclidean spaces. In recent decade this approach was also developed in the framework of the run-and-tumble theory. In this article we study one of the most important characteristics of the multidimensional symmetric Markov random flight, namely, its characteristic function. We derive two series representations of the characteristic function of the process with respect to Bessel functions with variable indices and with respect to the powers of time variable. The coefficients of these series are given by recurrent relations, as well as in the form of special determinants. As an application of these results, an asymptotic formula for the second moment function (mu _{(2,2,2)}(t), ; t>0,) of the three-dimensional Markov random flight, is presented. The moment function (mu _{(2,0,0)}(t), ; t>0,) is obtained in an explicit form.

The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with the in-flow, diffuse-reflection, or specular-reflection boundary condition. Using a novel kernel estimate, we demonstrate the optimal (L^2) diffusive limit in the presence of both initial and boundary layers. Previously, this result was only proved for convex domains when the time variable is involved. Our approach is highly robust, making it applicable to all basic types of physical boundary conditions.

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability (1-f(t)). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation (-gamma ), where (gamma in [0,1)). We also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

For (alpha ge 1), let (g:{mathbb {N}}rightarrow {mathbb {R}}_+) be given by (g(0)=0), (g(1)=1), (g(k)=(k/k-1)^alpha ), (kge 2). Consider the homogeneous zero range process on a discrete set in which a particle jumps from a site x, occupied by k particles, to site y with rate (g(k)p(y-x)) for some fixed probability (p:{mathbb {Z}}rightarrow [0,1]). Armendáriz and Loulakis (Probab Theory Relat Fields 145:175–188, 2009, https://doi.org/10.1007/s00440-008-0165-7) proved a strong form of the equivalence of ensembles for the invariant measure of the supercritical zero range process with (alpha >2). We generalize their result to all (alpha ge 1).

We rigorously prove that the local conserved quantities in the one-dimensional Hubbard model are uniquely determined for each locality up to the freedom to add lower-order ones. From this, we can conclude that the local conserved quantities are exhausted by those obtained from the expansion of the transfer matrix.

We present a statistical mechanical theory of multi-component fluids, where we consider the correlation functions of the number densities and the energy density in the grand canonical ensemble. In terms of their space integrals we express the partial volumes ({{bar{v}}}_i), the partial enthalpies ({{bar{H}}}_i), and other thermodynamic derivatives. These ({{bar{v}}}_i) and ({{bar{H}}}_i) assume simple forms for binary mixtures and for ternary mixtures with a dilute solute. They are then related to the space-dependent thermal fluctuations of the temperature and the pressure. The space averages of these fluctuations are those introduced by Landau and Lifshits in the isothermal-isobaric (T-p) ensemble. We also give expressions for the long-range (nonlocal) correlations in the canonical and T-p ensembles, which are inversely proportional to the system volume. For a mixture solvent, we examine the solvent-induced solute–solute attraction and the osmotic enthalpy changes due to the solute doping using the correlation function integrals.

Unlike the single species gases, the transport coefficients such as Fick, Soret, Dufour coefficients arise in the hydrodynamic limit of multi-species gas mixtures. To the best of the authors’ knowledge, no multi-component relaxational models is reported that produces all these values correctly. In this paper, we establish the existence of unique stationary mild solutions to the BGK models for gas mixtures which produces the correct Fick coefficients in the Navier–Stokes limit for inert gases (Brull in Eur J Mech B 33:74–86, 2012), and for reactive gases (Brull and Schneider in Commun Math Sci 12(7):1199–1223, 2014) in a unified manner.

In this work, we develop a mathematical framework to model a quantum system whose time evolution may depend on the state of a randomly changing environment that evolves according to a Markovian process. When the environment changes its state, three possible things may occur: the quantum system starts evolving according to a new Hamiltonian, it may suffer an instantaneous perturbation that changes its state or both things may happen simultaneously. We consider the case of quantum systems with finite dimensional Hilbert state space, in which case the observables are described by Hermitian matrices. We show how to average over the environment to predict the expected value of the density matrix with which one can compute the expected values of the observables of interest.

We consider the relaxation of an initial non-equilibrium state in a one-dimensional fluid of hard rods. Since it is an interacting integrable system, we expect it to reach the Generalized Gibbs Ensemble (GGE) at long times for generic initial conditions. Here we show that there exist initial conditions for which the system does not reach GGE even at very long times and in the thermodynamic limit. In particular, we consider an initial condition of uniformly distributed hard-rods in a box with the left half having particles with a singular velocity distribution (all moving with unit velocity) and the right half particles in thermal equilibrium. We find that the density profile for the singular component does not spread to the full extent of the box and keeps moving with a fixed effective speed at long times. We show that such density profiles can be well described by the solution of the Euler equations almost everywhere except at the location of the shocks, where we observe slight discrepancies due to dissipation arising from the initial fluctuations of the thermal background. To demonstrate this effect of dissipation analytically, we consider a second initial condition with a single particle at the origin with unit velocity in a thermal background. We find that the probability distribution of the position of the unit velocity quasi-particle has diffusive spreading which can be understood from the solution of the Navier–Stokes (NS) equation of the hard rods. Finally, we consider an initial condition with a spread in velocity distribution for which we show convergence to GGE. Our conclusions are based on molecular dynamics simulations supported by analytical arguments.