Journal of Statistical Physics最新文献

We consider a random field (phi ({textbf{r}})) in d dimensions which is largely concentrated around small ‘hotspots’, with ‘weights’, (w_i). These weights may have a very broad distribution, such that their mean does not exist, or is dominated by unusually large values, thus not being a useful estimate. In such cases, the median ({overline{W}}) of the total weight W in a region of size R is an informative characterisation of the weights. We define the function F by (ln {overline{W}}=F(ln R)). If (F'(x)>d), the distribution of hotspots is dominated by the largest weights. In the case where (F'(x)-d) approaches a constant positive value when (Rrightarrow infty ), the hotspots distribution has a type of scale-invariance which is different from that of fractal sets, and which we term ultradimensional. The form of the function F(x) is determined for a model of diffusion in a random potential.

Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results in which such relativistic BGK models for gas mixture are employed to compute transport coefficients. However, to the best knowledge of authors, relativistic BGK models for gas mixtures with complete presentation of the relaxation operators are missing in the literature. In this paper, we fill this gap by suggesting a BGK model for relativistic gas mixtures for which the existence of each equilibrium coefficients in the relaxation operator is rigorously guaranteed in a way that all the essential physical properties are satisfied such as the conservation laws, the H-theorem, the capturing of the correct equilibrium state, the indifferentiability principle, and the recovery of the classical BGK model in the Newtonian limit.

The Lillo–Mike–Farmer (LMF) model is an established econophysics model describing the order-splitting behaviour of institutional investors in financial markets. In the original article (Lillo et al. in Phys Rev E 71:066122, 2005), LMF assumed the homogeneity of the traders’ order-splitting strategy and derived a power-law asymptotic solution to the order-sign autocorrelation function (ACF) based on several heuristic reasonings. This report proposes a generalised LMF model by incorporating the heterogeneity of traders’ order-splitting behaviour that is exactly solved without heuristics. We find that the power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous order-submission probability distributions. On the other hand, the prefactor in the ACF is very sensitive to heterogeneity in trading strategies and is shown to be systematically underestimated in the original homogeneous LMF model. Our work highlights that predicting the ACF prefactor is more challenging than the ACF exponent because many microscopic details (complex ingredients in actual data analyses) start to matter.

Adding activity or driving to a thermal system may modify its phase diagram and response functions. We study that effect for a Curie–Weiss model where the thermal bath switches rapidly between two temperatures. The critical temperature moves with the nonequilibrium driving, opening up a new region of stability for the paramagnetic phase (zero magnetization) at low temperatures. Furthermore, phase coexistence between the paramagnetic and ferromagnetic phases becomes possible at low temperatures. Following the excess heat formalism, we calculate the nonequilibrium thermal response and study its behaviour near phase transitions. Where the specific heat at the critical point makes a finite jump in equilibrium (discontinuity), it diverges once we add the second thermal bath. Finally, (also) the nonequilibrium specific heat goes to zero exponentially fast with vanishing temperature, realizing an extended Third Law.

We analyse the motion of one particle in a polymer chain. For this purpose, we use the framework of the exact (non-stationary) generalized Langevin equation that can be derived from first principles via the projection-operator method. Our focus lies on determining memory kernels from either exact expressions for autocorrelation functions or from simulation data. We increase the complexity of the underlying system starting out from one-dimensional harmonic chains and ending with a polymer driven through a polymer melt. Here, the displacement or the velocity of an individual particle in the chain serves as the observable. The central result is that the time-window in which the memory kernels show structure before they rapidly decay decreases with increasing complexity of the system.

We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.

This paper is concerned with a modified entropy method to establish the large-time convergence towards the (unique) steady state, for kinetic Fokker–Planck equations with non-quadratic confinement potentials in whole space. We extend previous approaches by analyzing Lyapunov functionals with non-constant weight matrices in the dissipation functional (a generalized Fisher information). We establish exponential convergence in a weighted (H^1)-norm with rates that become sharp in the case of quadratic potentials. In the defective case for quadratic potentials, i.e. when the drift matrix has non-trivial Jordan blocks, the weighted (L^2)-distance between a Fokker–Planck-solution and the steady state has always a sharp decay estimate of the order (mathcal Obig ( (1+t)e^{-tnu /2}big )), with (nu ) the friction parameter. The presented method also gives new hypoelliptic regularization results for kinetic Fokker–Planck equations (from a weighted (L^2)-space to a weighted (H^1)-space).

We establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy–entropy production inequality from one case to the other; therefore providing entropy–entropy production inequalities for the Boltzmann–Fermi–Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csiszár–Kullback–Pinsker inequality to weighted (L^p) norms, (1 le p le 2) and a wide class of entropies.

A half-space problem of a linear kinetic equation for gas molecules physisorbed close to a solid surface, relevant to a kinetic model of gas–surface interaction and derived by Aoki et al. (Phys. Rev. E 106:035306, 2022), is considered. The equation contains a confinement potential in the vicinity of the solid surface and an interaction term between gas molecules and phonons. It is proved that a unique solution exists when the incoming molecular flux is specified at infinity. This validates the natural observation that the half-space problem serves as the boundary condition for the Boltzmann equation. It is also proved that the sequence of approximate solutions used for the existence proof converges exponentially fast. In addition, numerical results showing the details of the solution to the half-space problem are presented.

Granular gases demand models capable of capturing their distinct characteristics. The widely employed inelastic hard-sphere model (IHSM) introduces complexities that are compounded when incorporating realistic features like surface roughness and rotational degrees of freedom, resulting in the more intricate inelastic rough hard-sphere model (IRHSM). This paper focuses on the inelastic rough Maxwell model (IRMM), presenting a more tractable alternative to the IRHSM and enabling exact solutions. Building on the foundation of the inelastic Maxwell model (IMM) applied to granular gases, the IRMM extends the mathematical representation to encompass surface roughness and rotational degrees of freedom. The primary objective is to provide exact expressions for the Navier–Stokes–Fourier transport coefficients within the IRMM, including the shear and bulk viscosities, the thermal and diffusive heat conductivities, and the cooling-rate transport coefficient. In contrast to earlier approximations in the IRHSM, our study unveils inherent couplings, such as shear viscosity to spin viscosity and heat conductivities to counterparts associated with a torque-vorticity vector. These exact findings provide valuable insights into refining the Sonine approximation applied to the IRHSM, contributing to a deeper understanding of the transport properties in granular gases with realistic features.