Validity of the zero-thermodynamic law in off-equilibrium coupled harmonic oscillators

摘要

In order to describe the thermodynamics of the glassy systems it has beenrecently introduced an extra parameter also called effective temperature whichgeneralizes the fluctuation-dissipation theorem (FDT) to systemsoff-equilibrium and supposedly describes thermal fluctuations around the agingstate. Here we investigate the applicability of a zero-th law fornon-equilibrium glassy systems based on these effective temperatures bystudying two coupled subsystems of harmonic oscillators with Monte Carlodynamics. We analyze in detail two types of dynamics: 1) sequential dynamicswhere the coupling between the subsystems comes only from the Hamiltonian and2) parallel dynamics where there is a further coupling between the subsystemsarising from the dynamics. We show that the coupling described in the firstcase is not enough to make asymptotically the effective temperatures of twointeracting subsystems coincide, the reason being the too small thermalconductivity between them in the aging state. This explains why differentinteracting degrees of freedom in structural glasses may stay at differenteffective temperatures without never mutually thermalizing.