# Big Entropy Fluctuations in Statistical Equilibrium: The Macroscopic Kinetics Source: [Big Entropy Fluctuations in Statistical Equilibrium: The Macroscopic Kinetics]() Collection index: [llms.txt]() Data updated: 2025-10-24T10:11:18.939Z Authors: B.V. Chirikov, O.V. Zhirov Published: 2000-10-31T10:53:08.000Z ## Abstract Large entropy fluctuations in an equilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2--freedom strongly chaotic Hamiltonian model described by the modified Arnold cat map. The rise and fall of a large separated fluctuation was shown to be described by the (regular and stable) "macroscopic" kinetics both fast (ballistic) and slow (diffusive). We abandoned a vague problem of "appropriate" initial conditions by observing (in a long run)spontaneous birth and death of arbitrarily big fluctuations for any initial state of our dynamical model. Statistics of the infinite chain of fluctuations, reminiscent to the Poincar\\'e recurrences, was shown to be Poissonian. A simple empirical relation for the mean period between the fluctuations (Poincar\\'e "cycle") has been found and confirmed in numerical experiments. A new representation of the entropy via the variance of only a few trajectories ("particles") is proposed which greatly facilitates the computation, being at the same time fairly accurate for big fluctuations. The relation of our results to a long standing debates over statistical "irreversibility" and the "time arrow" is briefly discussed too. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()