Journal of Statistical Physics最新文献

In this work we investigate spectral properties of squared random matrices with independent entries that have only two finite moments. We revisit the problem of perturbing a large, i.i.d. random matrix by a finite rank error. We prove that under a merely second moment condition, for a large class of perturbation matrix with bounded rank and bounded operator norm, the outlier eigenvalues of perturbed matrix still converge to that of the perturbation, which was previously known when matrix entries have finite fourth moment. We then show that the same perturbation holds for very sparse random matrices with i.i.d. entries, all the way up to a constant number of nonzero entries per row and column.

In this paper we introduce, inspired by Clausius and developing the ideas of [11], the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory. Besides providing a new proof of a formula derived in [3, 4], which is the basis of the equivalence, we show that equivalent quasistatic transformations can be distinguished in finite terms, by the renormalized work introduced in [1,2,3,4]. This allows us to tackle the problem of determining the optimal quasistatic transformation among the equivalent ones.

Recently, the concept of minimal dissipation has been brought forward as a means to define work performed on open quantum systems [Phys. Rev. A 105, 052216 (2022)]. We discuss this concept from the point of view of projection operator formalisms in classical statistical physics. We analyse an autonomous composite system which consists of a system and an environment in the most general sense (i.e. we neither impose conditions on the coupling between system and environment nor on the properties of the environment). One condition any useful definition of work needs to fulfil is that it reproduces the thermodynamic notion of work in the limit of weak coupling to an environment that has infinite heat capacity. We propose a projection operator route to a definition of work that reaches this limit and we discuss its relation to minimal dissipation.

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.