Naslov
Introduction of MaxEnt algorithm to Hamiltonian dynamics of classical macroscopic closed systems

Autori
Kuić, Domagoj ; Županović, Paško

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Workshop programme and abstracts / - Jena, 2010, 19-19

Skup
Workshop on MAXIMUM ENTROPY PRODUCTION IN THE EARTH SYSTEM

Mjesto i datum
Jena, Njemačka, 10.05.2010. - 12.05.2010

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
MaxENT algorithm; Liouville equations; Hamiltonian dynamics; closed system; Jaynes

Sažetak
Possibility of application of MaxEnt algorithm to Hamiltonian dynamics of classical macroscopic closed systems is considered here in two approaches. The first approach is based on Liouville equations as strict microscopic constraints on time evolution of probability distributions in phase space. It is argued that this approach is equivalent to complete and objective information on microscopic dynamics. It is shown that it is possible to apply the MaxEnt algorithm consistently with this strict microscopic constraint, if the concepts of conditional probability distribution and respective conditional information entropy introduced by Shannon are utilized. Importance of phase space paths (solutions of Hamilton’s equations) is also emphasized. The second approach is also based on these concepts. Distinction between two approaches is in regarding the Liouville equation for conditional probability distribution as a macroscopic constraint in second approach, in accordance with Jaynes formulation of predictive statistical mechanics. It is shown that maximization of the conditional information entropy subject to this macroscopic constraint leads to a complete loss of correlation between the initial phase space paths and final microstates. During time evolution of the closed system, information entropy of the microstate probability distribution also becomes maximal. This happens indirectly, as a consequence of application of MaxEnt to the conditional information entropy. The former information entropy constitutes the upper bound on the latter, and the upper bound is attained only in case of the loss of correlation, or independence. It is shown therefore that if macroscopic time evolution is considered in this way these properties become equivalent.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

POVEZANOST RADA