Phase transition of a spin-lattice-gas model with two timescales and two temperatures

We study the phase transition of a nonequilibrium statistical-mechanical model, in which two degrees of freedom with different time scales separated from each other touch their own heat bath. A general condition for finding anomalous negative latent heat recently discovered is derived from a thermodynamic argument. As a specific example, the phase diagram of a spin-lattice-gas model is studied based on a mean-field analysis with the replica method. While configurational variables are spin and particle in this model, it is found that the negative latent heat appears in a parameter region of the model, irrespective of the order of their time scale. Qualitative differences in the phase diagram are also discussed.