Journal of Statistical Physics最新文献

In this paper, we consider the direct application of the relativistic extended thermodynamics theory of polyatomic gases developed in [Ann. Phys. 377 (2017) 414–445] to the relativistic BGK model proposed by Marle. We present the perturbed Marle model around the generalized Jüttner distribution and investigate the properties of the linear operator. Then we prove the global existence and large-time behavior of classical solutions when the initial data is sufficiently close to a global equilibrium.

In two dimensions, all isometrically invariant Markov random fields on binary assignments are induced by energy functions that can be represented as linear combinations of area, perimeter, and Euler characteristic. This class of model includes the Ising model, both ferro- and antiferromagnetic, with and without a field, as well as the Baxter-Wu model. On the hexagonal lattice, we determine the low-temperature behavior for this class of model, and construct a phase diagram of said behavior. In particular, we identify regions with three geometric phases, regions with a single unique phase, and coexistence curves between them. We also characterize the behavior along two non-Peierls lines, where entropy fails to vanish the as temperature goes to zero.

By modifying the automaton used by Pönitz and Tittman [9], principally by enabling multiple choices for state transitions through various simplification strategies, and considering states with a maximum size-loop of 26 (compared to 22 in their work), we obtain 2.662343 as an upper bound for the connective constant on the square lattice (mathbb {Z}^2).

Stochastic transport due to a velocity field modeled by the superposition of small-scale divergence free vector fields activated by Fractional Gaussian Noises (FGN) is numerically investigated. We present two non-trivial contributions: the first one is the definition of a model where different space-time structures can be compared on the same ground: this is achieved by imposing the same average kinetic energy to a standard Ornstein-Uhlenbeck approximation, then taking the limit to the idealized white noise structure. The second contribution, based on the previous one, is the discovery that a mixing spatial structure with persistent FGN in the Fourier components induces a classical Brownian diffusion of passive particles, with a suitable diffusion coefficient; namely, the memory of FGN is lost in the space complexity of the velocity field.

A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are conserved and kinetic energy is dissipated. Such a system can be described by a kinetic equation of the Boltzmann type. Nevertheless, due to the macroscopic aspect of the particles, any realistic description of a granular gas should be written as a mixture model composed of M different species, each with its own mass. We propose in this work such a granular multi-species model and analyse it, providing Povzner-type inequalities, and a Cauchy theory in general Orlicz spaces. We also analyse its large time behavior, showing that it exhibits a mixture analogue of the seminal Haff’s Law.

Originally proposed to model the adsorption of diatomic molecules on crystal surfaces, the monomer-dimer model has since found extensive applications in statistical mechanics and combinatorics. In this study, we examine mixtures of monomers and dimers on planar honeycomb lattices, focusing on the derivation of a generating function that enumerates all possible configurations as a function of monomer activity. We highlight the relevance of the Hosoya index in this context and introduce an expression for the matching polynomial specific to honeycomb structures. Furthermore, we investigate lozenge tilings of semiregular hexagons, which correspond bijectively to dimer coverings of honeycomb graphs. In particular, we provide a detailed combinatorial analysis of symmetric lozenge tilings of a hexagon with side lengths (m, m, n, m, m, n).

We calculate Jones polynomials (V(H_r,t)) for a family of alternating knots and links (H_r) with arbitrarily many crossings r, by computing the Tutte polynomials (T(G_+(H_r),x,y)) for the associated graphs (G_+(H_r)) and evaluating these with (x=-t) and (y=-1/t). Our method enables us to circumvent the generic feature that the computational complexity of (V(L_r,t)) for a knot or link (L_r) for generic t grows exponentially rapidly with r. We also study the accumulation set of the zeros of these polynomials in the limit of infinitely many crossings, (r rightarrow infty ).

We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation. For two large classes of fitness distributions of Gumbel type we determine the growth of the population, almost surely on survival. We then study the empirical fitness distribution in a simplified model, which is numerically indistinguishable from the original model, and show the emergence of a Gaussian travelling wave.

In this paper, we study reflecting Brownian motion with Poissonian resetting. After providing a probabilistic description of the phenomenon using jump diffusions and semigroups, we analyze the time-reversed process starting from the stationary measure. We prove that the time-reversed process is a Brownian motion with a negative drift and non-local boundary conditions at zero. Moreover, we further study the time-reversed process between two consecutive resetting points and show that, within this time window, it behaves as the same reflecting Brownian motion with a negative drift, where both the jump sizes and the time spent at zero coincide with those of the process obtained under the stationary measure. We characterize the dynamics of both processes, their local times, and finally investigate elliptic problems on positive half-spaces, showing that the two processes leave the same traces at the boundary.

The entropy production is commonly interpreted as measuring the distance from equilibrium. However, this explanation lacks a rigorous description due to the absence of a natural equilibrium measure. The present analysis formalizes this interpretation by expressing the entropy production of a Markov system as a divergence with respect to particular equilibrium dynamics. These equilibrium dynamics correspond to the closest reversible systems in the information-theoretic sense. This result yields novel links between nonequilibrium thermodynamics and information geometry.