Phenomenological determinism in Hamiltonian dynamical systems

A. Samain and X. Garbet

Physica A: Statistical Mechanics and its Applications, 2021, vol. 572, issue C

Abstract: Classical equations that govern the information in a Boltzmann–Gibbs Hamiltonian dynamical system are shown to entail the evolution of a phenomenological fraction of the information. The evolution of this fraction of information can be predicted along a preferential time direction provided a structural condition on the dynamics time scale is fulfilled. This preferential direction points towards the future or the past, starting from an initial time, provided an appropriate initial condition is fulfilled by the Boltzmann–Gibbs distribution at this time. Choosing one direction defines an arrow of time. That fraction of information is thus submitted to a phenomenological determinism. It permanently generates non-phenomenological components of the information, which accumulate, and experience an exponentially fast complexification. This complexification makes the accumulated non-phenomenological information unable to influence the evolution of the phenomenological information. That evolution is thus autonomous and deterministic.

Keywords: Irreversibility; Kinetic equations; Entropy (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437121001655
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:572:y:2021:i:c:s0378437121001655

DOI: 10.1016/j.physa.2021.125893

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().