Effective temperature in nonequilibrium state with heat flux using discrete variable model

The effective temperature, which acts as a criterion for thermalization in systems with heat flux, has been introduced on the bases of a relatively simple discrete variable model (DVM). The DVM is inherently nonlocal and can be used to describe multi-length and -time scale heat conduction including low-dimensional and sub-continuum regimes. Under far from equilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature and the corresponding nonequilibrium entropy go to zero, which points to a possible generalization of the third law in nonequilibrium situations.