A New Proof for a Metrically Transitive System

Hedlund, Gustav A.

doi:10.2307/2371449

Cited by 29 publications

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“…In fact, this is where the confusion in the consideration of reversible and irreversible dynamic chaos was born since it was in this place that the system was imposed with properties that it does not possess. The inaccuracy of the conclusions of many works was reduced to this (see, for example, [29,62,63,[83][84][85][86]). So, for example, when studying the divergence of the trajectories of elastically interacting balls, Krylov concludes [29] that their trajectories inevitably run up, forgetting that, for example, if we let the balls go in the opposite direction, then his consideration should lead to the convergence of the trajectories.…”

Section: Introduction 11 Status Of the Problem And Its Current Statementioning

confidence: 99%

The Transition to Equilibrium in a System with Gravitationally Interacting Particles. I. Temperature Relaxation

Boichenko

Klenovskii

2021

PSIJ

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The distribution function of systems in equilibrium must have the canonical form of the Gibbs distribution. To substantiate this behavior of systems, attempts have been made for more than 100 years to involve their mechanical behavior. In other words, it seems that a huge number of particles of the medium as a result of interaction with each other according to dynamic laws, is able to explain the statistical behavior of systems during their transition to equilibrium. Modeling of gravitationally interacting particles is carried out and it is shown that in this case, the distribution function does not evolve to the canonical form. Earlier, the same results were obtained for classical Coulomb plasma. On the other hand, such a statistical effect as relaxation is well described by the dynamic behavior of the system, and the simulation data are in agreement with the known theoretical results obtained in various statistical approaches.

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