Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the c ouplings are allowed to change with time. The spins are coupled to a heat b ath with temperature T, while the coupling constants are coupled to a bath having temperature T-J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two -temperature thermodynamics. It involves entropies of the spins and the cou pling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n = T/T-J. For p > 2 there occur at low temperatures two different glassy phases, depending o n the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentia lly non-equilibrium effect. The dynamical phase transition exists only for n < 1. For p 2 correlation of the disorder (leading to a non-zero n) remove s the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived.