2013/02/02 by Yu. E. Kuzovlev, Kuzovlev, Yu. E.
Physics and Astronomy · Economics, Econometrics and Finance · #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy #Complex Systems and Time Series Analysis
paper · pdf · doi:10.48550/arxiv.1302.0373
Dynamical random walk of classical particle in thermodynamically equilibrium\nfluctuating medium, - Gaussian random potential field, - is considered in the\nframework of explicit stochastic representation of deterministic interactions.\nWe discuss corresponding formally exact Langevin equations for the particle's\ntrajectory and show that Marcovian kinetic equation approximation to them is\ninadequate, - even (and especially) in case of spatially-temporally\nshort-correlated field, - since ignores such actual effects of exponential\ninstability of the trajectory (in respect to small perturbations) as scaleless\nlow-frequency diffusivity/mobility fluctuations (and other excess degrees of\nrandomness) reflected by third-, fourth- and higher-order long-range\nirreducible statistical correlations. We try to catch the latter, - squeezing\nthrough typical theoretical narrow bottleneck, - with the help of an exact\nrelationship between the instability and diffusivity statistical\ncharacteristics, along with standard analytical d approximations. The result is\nquasi-static diffusivity fluctuations which generally are comparable with mean\nvalue of diffusivity and disappear in the limit of infinitely large medium's\ncorrelation length or infinitely small correlation time only, in agreement with\nthe previously suggested theorem on fundamental 1/f noise.\n