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

Abstract:

In order to describe the thermodynamics of the glassy systems it has been recently introduced an extra parameter, the effective temperature which generalizes the fluctuation-dissipation theorem (FDT) to off-equilibrium systems and supposedly describes thermal fluctuations around the aging state. Using this concept we investigate the applicability of a zeroth thermodynamic law for non-equilibrium systems. In particular we study two coupled systems of harmonic oscillators with Monte Carlo dynamics. We analyze in detail two types of dynamics: 1) sequential dynamics where the coupling between the subsystems comes only from the Hamiltonian and 2) parallel dynamics where there is a further coupling between the subsystems arising from the dynamics. We show that the coupling described in the first case is not enough to make asymptotically the effective temperatures of the two interacting subsystems equalize, the reason being the too small thermal conductivity between them in the aging state. This explains why different interacting degrees of freedom in structural glasses may stay at different effective temperatures without never mutually thermalizing.