Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation–dissipation theorem (FDT). This hierarchy means that ergodicity...

The dynamics of temperature fluctuations of a gas of Brownian particles in local equilibrium with a nonequilibrium heat bath are described using an approach consistent with Boltzmann–Gibbs (BG) statistics. We use mesoscopic nonequilibrium thermodynamics (MNET) to derive a Fokker–Planck...