Fractional kinetics: from pseudochaotic dynamics to Maxwell’s Demon

In Hamiltonian dynamics chaotic trajectories can be characterized by a non-zero Lyapunov exponent. In general case of random dynamics the Lyapunov exponent can be close to zero because of the stickiness, or simply zero, as in the case of pseudochaos. Kinetic description of such situations is based on scaling properties of the dynamics in both space and time. It is shown for different models that the ergodic theorem cannot be applied for the observed data, and that weak mixing leads to unusual macroscopic behavior. Such phenomenon as Maxwell’s Demon obtains a natural realization as a persistent fluctuation that does not decay in an exponential way as in the kinetics of the Gaussian type.