Journal of Statistical Physics最新文献

We conducted a comprehensive numerical investigation of the energy landscape of the Thomson problem for systems up to (N=150). Our results show the number of distinct configurations grows exponentially with N, but significantly faster than previously reported. Furthermore, we find that the average energy gap between independent configurations at a given N decays exponentially with N, dramatically increasing the computational complexity for larger systems. Finally, we developed a novel approach that reformulates the search for stationary points in the Thomson problem (or similar systems) as an equivalent minimization problem using a specifically designed potential. Leveraging this method, we performed a detailed exploration of the solution landscape for (Nle 24) and estimated the growth of the number of stationary states to be exponential in N.

Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is at rest and the other one oscillates in its normal direction periodically in time. For such boundary-value problem, we establish the existence of a time-periodic solution with the same period, provided that the amplitude of the oscillating boundary is suitably small. The positivity of the solution is also proved basing on the study of its large-time asymptotic stability for the corresponding initial-boundary value problem. For the proof of existence, we develop uniform estimates on the approximate solutions in the time-periodic setting and make a bootstrap argument by reducing the coefficient of the extra penalty term from a large enough constant to zero.

Traditionally, fractional counting processes, such as the fractional Poisson process etc., have been defined using three methods: (i) through fractional differential and integral operators, (ii) by employing non-exponential waiting times in the renewal process approach, and (iii) by time-changing the Poisson process. Recently, Laskin (2024) introduced a broader class of fractional counting processes (FCP) by introducing the methodology for direct construction of the probability distribution using generalized three-parameter Mittag-Leffler function. In this paper, we introduce the time-changed fractional counting process (TCFCP), defined by time-changing the FCP with an independent Lévy subordinator. We derive distributional properties and results related to first waiting and the first passage time distribution are also discussed. We define the additive and multiplicative compound variants for the FCP and the TCFCP and examine their distributional characteristics with some typical examples. We explore some interesting connections of the TCFCP with Bell polynomials by introducing subordinated generalized fractional Bell polynomials. Finally, we present the application of the TCFCP in a shock deterioration model.

We consider the simple random walk on (mathbb {Z}^d) killed with probability p(|x|) at site x for a function p decaying at infinity. Due to recurrence in dimension (d=2), the killed random walk (KRW) dies almost surely if p is positive, while in dimension (d ge 3) it is known that the KRW dies almost surely if and only if (int _0^{infty }rp(r)dr = infty ), under mild technical assumptions on p. In this paper we consider, for any (d ge 2), functions p for which the random walk will die almost surely and we ask ourselves if the KRW conditioned to survive is well-defined. More precisely, given an exhaustion ((Lambda _R)_{R in mathbb {N}}) of (mathbb {Z}^d), does the KRW conditioned to leave (Lambda _R) before dying converges in distribution towards a limit which does not depend on the exhaustion? We first prove that this conditioning is well-defined for (p(r) = o(r^{-2})), and that it is not for (p(r) = min (1, r^{-alpha })) for (alpha in (14/9,2)). This question is connected to branching random walks and the infinite snake. More precisely, in dimension (d=4), the infinite snake is related to the KRW with (p(r) asymp (r^2log (r))^{-1}), therefore our results imply that the infinite snake conditioned to avoid the origin in four dimensions is well-defined.

We study the first-passage dynamics of a non-Markovian stochastic process with time-averaged feedback, which we model as a one-dimensional Ornstein–Uhlenbeck process wherein the particle drift is modified by the empirical mean of its trajectory. This process maps onto a class of self-interacting diffusions. Using weak-noise large deviation theory, we calculate the leading order asymptotics of the time-dependent distribution of the particle position, derive the most probable paths that reach the specified position at a given time and quantify their likelihood via the action functional. We compute the feedback-modified Kramers rate and its inverse, which approximates the mean first-passage time, and show that the feedback accelerates dynamics by storing finite-time fluctuations, thereby lowering the effective energy barrier and shifting the optimal first-passage time from infinite to finite. Although we identify alternative mechanisms, such as slingshot and ballistic trajectories, we find that they remain sub-optimal and hence do not accelerate the dynamics. These results show how memory feedback reshapes rare event statistics, thereby offering a mechanism to potentially control first-passage dynamics.

We consider a multi component gas mixture with translational and internal energy degrees of freedom without chemical reactions assuming that the number of particles of each species remains constant. We will illustrate the derived model in the case of two species, but the model can be generalized to multiple species. The two species are allowed to have different degrees of freedom in internal energy and are modeled by a system of kinetic Fokker-Planck equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the temperatures, H-theorem and we characterize the equilibrium as two Maxwell distributions where all temperatures coincide.

We study the statistics of first passage times (FPTs) of trajectory observables in both classical and quantum Markov processes. We consider specifically the FPTs of counting observables, that is, the times to reach a certain threshold of a trajectory quantity which takes values in the positive integers and is non-decreasing in time. For classical continuous-time Markov chains we rigorously prove: (i) a large deviation principle (LDP) for FPTs, whose corollary is a strong law of large numbers; (ii) a concentration inequality for the FPT of the dynamical activity, which provides an upper bound to the probability of its fluctuations to all orders; and (iii) an upper bound to the probability of the tails for the FPT of an arbitrary counting observable. For quantum Markov processes we rigorously prove: (iv) the quantum version of the LDP, and subsequent strong law of large numbers, for the FPTs of generic counts of quantum jumps; (v) a concentration bound for the the FPT of total number of quantum jumps, which provides an upper bound to the probability of its fluctuations to all orders, together with a similar bound for the sub-class of quantum reset processes which requires less strict irreducibility conditions; and (vi) a tail bound for the FPT of arbitrary counts. Our results allow to extend to FPTs the so-called “inverse thermodynamic uncertainty relations” that upper bound the size of fluctuations in time-integrated quantities. We illustrate our results with simple examples.

A new phase space path integral representation of quantum density of states (DOS) was derived for a strongly coupled plasma media representing hydrogen plasma and two-component Coulomb system with uniformly distributed in space uncorrelated positive charges (“protons”) simulating a neutralizing background (“OCP”). A path integral Monte Carlo approach was used for the calculation of DOS, energy and momentum distribution functions as well as spin–resolved radial distribution functions (RDFs). The RDFs for electrons with the same spin projection revealed exchange–correlation cavities. For a two-component hydrogen plasma (TCP) the Coulomb attraction results in the appearance of high peaks on the proton–electron RDFs at small interparticle distances, while for the “OCP” the analogous RDFs demonstrate an unexpected significant drop arising due to a three–particle effect caused by the electron repulsion preventing for any two electrons to be in the vicinity of any uncorrelated charge. At negative plasma energy the “OCP” DOS is a fast-decaying function, while in hydrogen plasma at a temperature of the order of 1 (textrm{Ry} = 0.5text {Ha}approx 13.6) eV the DOS shows a well-pronounced peak related to the bound states. Quantum effects make momentum distribution functions non-maxwellian with a power-law high-momentum asymptotics (“quantum tails”) even under the condition of thermodynamic equilibrium.

We study the Poisson Boolean percolation model on Ahlfors regular metric measure spaces, extending fundamental results from the Euclidean spaces to more general geometric settings. Ahlfors regular space is a metric measure space that has a polynomial growth rate of metric balls. Our main result establishes that for s-Ahlfors regular spaces, the model exhibits a subcritical regime (no infinite clusters for small intensities) if and only if the radius distribution has a finite s-th moment, generalizing Gouéré’s result for the Euclidean spaces. We prove both directions: when an s-th moment is finite, we show that subcritical behavior exists using geometric properties of Ahlfors regular spaces, particularly the doubling property and the uniform perfectness. Conversely, when an s-th moment diverges, we demonstrate that infinite clusters occur almost surely for any positive intensity. The key technical innovation lies in handling the geometric challenges absent in Euclidean spaces, such as potentially empty annuli between concentric balls. We overcome this using uniform perfectness, which guarantees nonempty annuli under sufficient expansion, combined with doubling properties to control covering numbers. Our results apply broadly to Riemannian manifolds with nonnegative Ricci curvature, ultrametric spaces, unbounded Sierpinski gaskets, and snowflake constructions of Ahlfors regular spaces.

Run-and-Tumble Particles (RTPs) are a key model of active matter. They are characterized by alternating phases of linear travel and random direction reshuffling. By this dynamic behavior, they break time reversibility and energy conservation at the microscopic level. It leads to complex out-of-equilibrium phenomena such as collective motion, pattern formation, and motility-induced phase separation (MIPS). In this work, we study two fundamental dynamical models of a pair of RTPs with jamming interactions and provide a rigorous link between their discrete- and continuous-space descriptions. We demonstrate that as the lattice spacing vanishes, the discrete models converge to a continuous RTP model on the torus, described by a Piecewise Deterministic Markov Process (PDMP). This establishes that the invariant measures of the discrete models converge to that of the continuous model, which reveals finite mass at jamming configurations and exponential decay away from them. This indicates effective attraction, which is consistent with MIPS. Furthermore, we quantitatively explore the convergence towards the invariant measure. Such convergence study is critical for understanding and characterizing how MIPS emerges over time. Because RTP systems are non-reversible, usual methods may fail or are limited to qualitative results. Instead, we adopt a coupling approach to obtain more accurate, non-asymptotic bounds on mixing times. The findings thus provide deeper theoretical insights into the mixing times of these RTP systems, revealing the presence of both persistent and diffusive regimes.