Statistical physics and fluctuations in ballistic non-equilibrium systems

In nonequilibrium systems in the ballistic transport regime, every point of the system contains particles arriving from different regions–each of them at different temperatures–and there are only few collisions, in such a way that equilibrium between the different populations will be reached very slowly. Here, we tentatively approach the local distribution function by a superposition of local-equilibrium distribution functions with different temperatures, corresponding to the different starting positions of the particles. In a second-order expansion, we find a distribution function which depends not only on the Hamiltonian H but also on H2, and we study the additional contribution to energy fluctuations