Journal of Statistical Physics最新文献

Applying a time-periodic magnetic field to the standard ferromagnetic Curie–Weiss model brings the spin system in a steady out-of-equilibrium condition. We recall how the hysteresis gets influenced by the amplitude and the frequency of that field, and how an amplitude- and frequency-dependent (dynamical) critical temperature can be discerned. The dissipated power measures the area of the hysteresis loop and changes with temperature. The excess heat determines a nonequilibrium specific heat giving the quasistatic thermal response. We compute that specific heat, which appears to diverge at the critical temperature, quite different from the equilibrium case.

A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a Hohenberg–Kohn theorem that manifests the magnetization and displacement as internal variables, along with several representability results. The constrained-search functionals for pure states and ensembles are introduced and analyzed. We find the optimizers for the pure-state constrained-search functional to be low-lying eigenstates of the Hamiltonian and, based on the properties of the optimizers, we formulate an adiabatic-connection formula. In the reduced case of the Rabi model we can even show differentiability of the universal density functional, which amounts to unique pure-state v-representability.

In this paper, the rotational entropy (h_r(varphi )) is investigated for a random dynamical system (varphi ) on the torus. The formula of (h_r(varphi )) is obtained for (varphi ) which satisfies certain assumptions, and the lower and upper bounds of (h_r(varphi )) are given for more general (varphi ). Several examples are presented to show that these results may not hold without the assumptions. This work can be seen as a random version of the previous work (Jiang et al. in J Differ Equ 379:862–883, 2024), in which the rotational entropy was introduced and investigated as a homotopy invariant for any torus map.

As an extension of weighted entropy, the weighted topological sequence entropy and the weighted measure-theoretic sequence entropy are defined. A variational principle of relating the two weighted sequence entropies is established. The weighted maximal pattern entropy is also defined. It is shown that for homeomorphism dynamical systems the weighted maximal pattern entropy is equal to the supremum of the weighted sequence entropies over all strictly increasing sequences in integers both in topological and measure-theoretic settings.

A multi-species Fokker–Planck model for simulating particle collisions in a plasma is presented. The model includes various parameters that must be tuned. Under reasonable assumptions on these parameters, the model satisfies appropriate conservation laws, dissipates an entropy, and satisfies an (mathcal {H})-Theorem. In addition, the model parameters provide the additional flexibility that is used to match simultaneously momentum and temperature relaxation formulas derived from the Boltzmann collision operator for a binary mixture with Coulomb potential. A numerical method for solving the resulting space-homogeneous kinetic equation is presented and two examples are provided to demonstrate the relaxation of species bulk velocities and temperatures to their equilibrium values.

We investigate the intertwining of Laguerre processes of parameter (alpha ) in different dimensions. We introduce a Feller kernel that depends on (alpha ) and intertwines the (alpha )-Laguerre process in (N+1) dimensions and that in N dimensions. When (alpha ) is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order ((N+alpha +1) times (N+1)) are fixed, then the those of its ((N+alpha ) times N ) truncation matrix are given by the new kernel.

The Trajectory Class Fluctuation Theorem (TCFT) presents equalities between thermodynamic quantities, such as work costs and free energy changes, and the probabilities of classes of system-state trajectories in equilibrium-steady-state nonequilibrium processes. Conceptually, the TCFT unifies a host of previously-established fluctuation theorems, interpolating from Crooks’ Detailed Fluctuation Theorem (single trajectories) to Jarzynski’s Equality (full trajectory ensembles). Leveraging coarse-grained information about how systems evolve, the TCFT provides a substantial strengthening of the Second Law of Thermodynamics—that, in point of fact, can be a rather weak bound between requisite work and free energy change. It also can be used to improve empirical estimates of free energies, a task known to be statistically challenging, by diverting attention from rare, work-dominant trajectories in convenient but highly nonequilibrium processes. The TCFT also reveals new forms of free energy useful for bounding work costs when computing with systems whose microscopic details are difficult to ascertain—forms that can be solved analytically and practically estimated. For engineered systems more generally, it connects the role of system state trajectories in system functionality to the particular work costs required to evolve those trajectories. Previously, the TCFT was used to connect the microscopic dynamics of experimentally-implemented Josephson-junction information engines with the mesoscopic descriptions of how information was processed. The development here justifies that empirical analysis, explicating its mathematical foundations.

We are concerned with the boundary layer problem for steady relativistic Boltzmann equation in half-space. By introducing some special test functions and choosing suitable estimate orders, we derive a crucial bound on the macroscopic part (textbf{P}f). Under certain admissible conditions and assuming exponential decay for the source term, we demonstrate the existence, continuity and the exponential spacial decay of a boundary layer solution for both linear and nonlinear steady relativistic Boltzmann equations with hard potential collision kernel. The uniqueness is also established under specific constraint conditions.

In molecular dynamics, transport coefficients measure the sensitivity of the invariant probability measure of the stochastic dynamics at hand with respect to some perturbation. They are typically computed using either the linear response of nonequilibrium dynamics, or the Green–Kubo formula. The estimators for both approaches have large variances, which motivates the study of variance reduction techniques for computing transport coefficients. We present an alternative approach, called the transient subtraction technique (inspired by early work by Ciccotti and Jaccucci in Phys Rev Lett 35(12):789–792, 1975, https://doi.org/10.1103/PhysRevLett.35.789), which amounts to simulating a transient dynamics started off equilibrium and relaxing towards the equilibrium state, from which we subtract a sensibly coupled equilibrium trajectory, resulting in an estimator with smaller variance. We present the mathematical formulation of the transient subtraction technique, give error estimates on the bias and variance of the associated estimator, and demonstrate the relevance of the method through numerical illustrations for various systems.

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.