Temperature Evolution in an Isolated Long Range Hamiltonian System

LUIS G. MOYANO; FULVIO BALDOVIN; CONSTANTINO TSALLIS

Caxambu, Minas Gerais

Encuentro; XXVI Encontro Nacional de Física da Matéria Condensada; 2003

SBF

The thermodynamics and the dynamics of isolated systems with infinite-range coupling display several unusual features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a paradigmatic example of this class of systems. The model corresponds to a system of N planar rotators, with every pair of spins coupled through a cosine potential term. The dynamical behavior of the model has been investigated in the microcanonical ensemble by starting the system out-of-equilibrium and integrating numerically the equations of motion. We use a type of out-of- equilibrium initial conditions (called water-bag initial conditions), which consist in all angles set to zero and a uniform momenta distribution. There is a certain region of energies immediately below the critical energy of the system that present deviations from the canonical ensemble theoretical predictions. After a brief transient the system reaches a meta-stable state (called Quasi-stationary state: QSS) which has important differences with the canonical equilibrium prediction. Finally, after a certain period of time the system reaches the predicted Boltzmannian stationary equilibrium state. In the meta-esquilibrium state, it has been found that the dynamics is known to be characterized by L´evy walks, anomalous diffusion, negative specific heat and aging. In this work we study, through numerical simulations, the dynamics of the system, focusing on the evolution of the mean kinetic energy per particle, proportional to the dynamical temperature of the system. We modeled the evolution of two systems, one considerably larger than the other, put into contact after a certain time, and studied the time evolution of their dynamical temperatures, in order to study the validity of the zeroth principle of thermodynamics in the meta-equilibrium state. The scenario is consistent with nonextensive statistical mechanics.