Nonlinear heat equation and two-level diffusion

The interaction between the diffusion of a Brownian particle which can occupy two energy levels, and the heat flow described by the Streater nonlinear heat equation, cf. [1], is analysed. Particularly, the Streater effect in which the potential energy of a particle is converted to heat due to friction is taken into account. It is shown that for such a continuum, the first law of thermodynamics and the modified form of the second law hold true, while the Prigogine conjecture is not satisfied even in the approximation known from a one level diffusion. Also, the behaviour of a system in isothermal conditions beyond a detailed balance is considered.