Journal of Statistical Physics最新文献

Asymptotic analyses of the Boltzmann equation for near-continuum low-Mach-number gas flows predominantly assume diffuse scattering from solid surfaces, i.e., complete surface accommodation, despite gas scattering often deviating from this idealized behavior in practice. While some results for arbitrary surface accommodation exist to second order in small Knudsen number, the full theory to this order is yet to be reported. Here, we present a matched asymptotic expansion of the linearized Boltzmann–BGK equation that generalizes existing theories to Maxwell-type boundary conditions with arbitrary accommodation at solid surfaces. This is performed to second order in small Knudsen number for smooth solid surfaces, and holds for steady and unsteady flow at oscillatory frequencies far smaller than the molecular collision frequency. In contrast to diffuse scattering, we find that the second-order Knudsen layer functions vary as (eta log ^2eta ) for incomplete but arbitrary accommodation at a curved surface, where (eta ) is the dimensionless normal coordinate. A modified refined moment method is developed to numerically handle this spatial dependency. Analytical formulas for all velocity slip and temperature jump coefficients for the Hilbert region are reported that exhibit accuracies greater than 99.9%. This resolves conflicting literature reports on the second-order velocity slip and temperature jump coefficients.

We consider the edge-triangle model (also known as the Strauss model) and its mean-field approximation, within the region of parameters called replica symmetric regime. While our motivation stems from analyzing the asymptotic behavior of the triangle density in the edge-triangle model, a significant part of our work is devoted to studying an approximation of this observable in the mean-field setting, where explicit computations are possible. More specifically, for the first model, we prove that the triangle density concentrates with high probability in a neighborhood of its typical values. For the second model we can go further and prove, for the approximated triangle density, a standard and non-standard central limit theorem at the critical point, still not known for the edge-triangle model. Additionally, we obtain many concentration results derived via large deviations and statistical mechanics techniques. Although a rigorous comparison between these two models is still lacking, we believe that they are asymptotically equivalent in many respects. To support this conjectured behavior, we complement the analysis with simulations related to the central limit theorem for the edge-triangle model.

Quantum correlation in bipartite systems has been extensively studied, and in recent years, people have been interested in the study of multipartite systems. Studying quantum correlations in local multipartite systems has also become a hot topic. In this paper, we define the local bipartite conditional mutual information, and further give the definitions of local multipartite interaction (common) information and local genuinely multipartite quantum mutual information. Then, we mainly study some properties and special relations of local genuinely multipartite quantum mutual information satisfaction. A special property that is different from the nonlocal case is that the local genuinely multipartite quantum mutual information may change under the local unitary operation. This is caused by the fact that the unitary operation may change the position of the particles.

In this paper, we study the stationary states of diffusive dynamics driven out of equilibrium by reservoirs. For a small forcing, the system remains close to equilibrium and the large deviation functional of the density can be computed perturbatively by using the macroscopic fluctuation theory. This applies to general domains in (mathbb {R}^d) and diffusive dynamics with arbitrary transport coefficients. As a consequence, one can analyse the correlations at the first non trivial order in the forcing and show that, in general, all the long range correlation functions are not equal to 0, in contrast to the exactly solvable models previously known.

In nonequilibrium systems with uncoupled currents, the thermodynamic affinity determines the direction of currents, quantifies dissipation, and constrains current fluctuations. However, these properties of the thermodynamic affinity do not hold in complex systems with multiple coupled currents. For this reason, there has been an ongoing search in nonequilibrium thermodynamics for an affinity-like quantity, known as the effective affinity, which applies to a single current in a system with multiple coupled currents. Here, we introduce an effective affinity that applies to generic currents in time-homogeneous Markov processes. We show that the effective affinity is a single number encapsulating several dissipative and fluctuation properties of fluctuating currents: the effective affinity determines the direction of flow of the current; the effective affinity multiplied by the current is a lower bound for the rate of dissipation; for systems with uncoupled currents the effective affinity equals the standard thermodynamic affinity; and the effective affinity constrains negative fluctuations of currents, namely, it is the exponential decay constant of the distribution of current infima. We derive the above properties with large deviation theory and martingale theory, and one particular interesting finding is a class of martingales associated with generic currents. Furthermore, we make a study of the relation between effective affinities and stalling forces in a biomechanical model of motor proteins, and we find that both quantities are approximately equal when this particular model is thermodynamically consistent. This brings interesting perspectives on the use of stalling forces for the estimation of dissipation.

Bose–Einstein condensation occurs when bosons aggregate to effectively form a single megaparticle. Analyses of Bose–Einstein condensation have generally assumed a bath with a temperature, i.e., a thermal equilibrium where random collisions lead to a Gaussian-noise-term. However, many setups in physics involve conversion or transport of energy, i.e., nonequilibrium. Nonequilibrium noise is commonly characterized by the frequent occurrence of large kicks and, as such, can be effectively modeled by the implementation of (alpha )-stable noise, also called Lévy noise. No temperature exists in that case. We analyze the simple case of bosons in a double-well potential subjected to (alpha )-stable noise. A formula for the distribution over the two wells is derived. It is found that Bose–Einstein condensation can still occur, but is probably much harder to engineer. Our results could be significant for understanding the obviously nonequilibrium quark-gluon plasmas that form after high-energy collisions of heavy nuclei.

We consider the classical trapped Riesz gas, i.e., N particles at positions (x_i) in one dimension with a repulsive power law interacting potential (propto 1/|x_i-x_j|^{k}), with (k>-2), in an external confining potential of the form (V(x) sim |x|^n). We focus on the equilibrium Gibbs state of the gas, for which the density has a finite support ([-ell _0/2,ell _0/2]). We study the fluctuations of the linear statistics ({{mathcal {L}}}_N = sum _{i=1}^N f(x_i)) in the large N limit for smooth functions f(x). We obtain analytic formulae for the cumulants of ({{mathcal {L}}}_N) for general (k>-2). For long range interactions, i.e. (k<1), which include the log-gas ((k rightarrow 0)) and the Coulomb gas ((k =-1)) these are obtained for monomials (f(x)= |x|^m). For short range interactions, i.e. (k>1), which include the Calogero–Moser model, i.e. (k=2), we compute the third cumulant of ({{mathcal {L}}}_N) for general f(x) and arbitrary cumulants for monomials (f(x)= |x|^m). We also obtain the large deviation form of the probability distribution of ({{mathcal {L}}}_N), which exhibits an “evaporation transition” where the fluctuation of ({{mathcal {L}}}_N) is dominated by the one of the largest (x_i). In addition, in the short range case, we extend our results to a (non-smooth) indicator function f(x), obtaining thereby the higher order cumulants for the full counting statistics of the number of particles in an interval ([-L/2,L/2]). We show in particular that they exhibit an interesting scaling form as L/2 approaches the edge of the gas (L/ell _0 rightarrow 1), which we relate to the large deviations of the emptiness probability of the complementary interval on the real line.

Recently, Tsukamoto (New approach to weighted topological entropy and pressure, Ergod Theory Dyn Syst 43:1004–1034, 2023) introduces a new approach to defining weighted topological entropy and pressure. Inspired by the ideas of Tsukamoto, we define the relative weighted topological entropy and pressure for factor maps and establish several variational principles. One of these results relate to a question raised by Feng and Huang (Variational principle for weighted topological pressure, J Math Pures Appl 106:411–452, 2016), namely, whether there exists a relative version of the weighted variational principle. In this paper, we try to establish such a variational principle. Furthermore, we generalize the Ledrappier and Walters type relative variational principle to the weighted version.

In their recent works [Comm Math Phys 399:367–388 (2023)] and [Comm Math Phys 406:32 (2025)], Michelen and Perkins proved that the pressure of a system of particles with repulsive pair interactions is analytic for activities in a complex neighborhood of ([0,eDelta _{phi }(beta )^{-1})), where (Delta _{phi }(beta )in (0,C_{phi }(beta )]) denotes what they call the potential-weighted connective constant. This paper extends their method to locally stable (possibly attractive), tempered, and hard-core pair potentials. We obtain an analogous analyticity result that is most effective in the high-temperature regime, where it surpasses the classical Penrose-Ruelle bound of (C_{phi }(beta )^{-1}e^{-(beta C+1)}) by at least a factor of (e^{2}). The main ingredients in the proof include a recursive identity for the one-point density tailored to locally stable hard-core potentials and a corresponding notion of modulations of an activity function.

We consider an abstract non-inertial model of aggregation under the influence of a Gaussian white noise with prescribed space-covariance, and prove a formula for the mean collision rate R, per unit of time and volume. Specializing the abstract theory to a non-inertial model obtained by an inertial one, with physical constants, in the limit of infinitesimal relaxation time of the particles, and the white noise obtained as an approximation of a Gaussian noise with correlation time (tau _{eta }), up to approximations the formula reads (Rsim tau _{eta }leftlangle left| Delta _{a}uright| ^{2}rightrangle acdot n^{2}) where n is the particle number per unit of volume and (leftlangle left| Delta _{a}uright| ^{2}rightrangle ) is the square-average of the increment of random velocity field u between points at distance a, the particle radius. If we choose the Kolmogorov time scale (tau _{eta }sim left( frac{nu }{varepsilon }right) ^{1/2}) and we assume that a is in the dissipative range where (leftlangle left| Delta _{a}uright| ^{2}rightrangle sim left( frac{varepsilon }{nu }right) a^{2}), we get Saffman–Turner formula for the collision rate R.