Dipolar needles in the microcanonical ensemble: evidence of spontaneous magnetization and ergodicity breaking

Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble Averages

Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs' canonical distribution for simple ( small ) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an ergodic isothermal dynamics to a harmonic oscillator, to a quartic oscillator, and even to the "Mexican-Hat" ( double-well ) potential problem. We consider here a time-reversible dynamical approach to Gibbs' "microcanonical" ( isoenergetic ) distribution for simple systems. To enable isoenergetic ergodicity we add occasional random rotations to the velocities. T…

非平衡动力学中离散非线性薛定谔方程过渡的动力学序参量

A dynamical order parameter for the transition to nonergodic dynamics in the discrete nonlinear Schrödinger equation

研究提出通过Kolmogorov-Sinai熵的渐近集合方差作为序参量，检测离散非线性薛定谔方程中平衡性破坏的转变特征。

Statistical mechanics and dynamics of solvable models with long-range interactions

The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^α$, with $α\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics, two-dimensional elasticity, charged and dipolar systems. Although such systems can be made extensive, they are intrinsically non additive. Moreover, the space of accessible macroscopic thermodynamic parameters might be non convex. The violation of these two basic properties is at the origin of ensemble inequivalence, which implies that specific heat can be negative in t…

Ensemble Inequivalence in the Ferromagnetic p-spin Model in Random Fields

We study the effect that randomness has on long-range interacting systems by using the ferromagnetic Ising model with $p$-body interactions in random fields. The case with p=2 yields a phase diagram similar to that of previously studied models and shows known features that inequivalence of the canonical and microcanonical ensembles brings with it, for example negative specific heat in a narrow region of the phase diagram. When p>2, however, the canonical phase diagram is completely different from the microcanonical one. The temperature does not necessarily determine the microcanonical phases u…

Edwards thermodynamics of the jamming transition for frictionless packings: ergodicity test and role of angoricity and compactivity

This paper illustrates how the tools of equilibrium statistical mechanics can help to explain a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J-point). Using the ensemble formalism we elucidate the following: (i)We test the combined volume-stress ensemble by comparing th…

Thermodynamics of the HMF model with a magnetic field

We study the thermodynamics of the Hamiltonian Mean Field (HMF) model with an external potential playing the role of a "magnetic field". If we consider only fully stable states, this system does not present any phase transition. However, if we take into account metastable states (for a restricted class of perturbations), we find a very rich phenomenology. In particular, the system displays a region of negative specific heats in the microcanonical ensemble in which the temperature decreases as the energy increases. This leads to ensembles inequivalence and to zeroth order phase transitions simi…