The Approach Towards Equilibrium in a Reversible Ising Dynamics Model: An Information-Theoretic Analysis Based on an Exact Solution
Artikel i vetenskaplig tidskrift, 2017

We study the approach towards equilibrium in a dynamic Ising model, the Q2R cellular automaton, with microscopic reversibility and conserved energy for an infinite one-dimensional system. Starting from a low-entropy state with positive magnetisation, we investigate how the system approaches equilibrium characteristics given by statistical mechanics. We show that the magnetisation converges to zero exponentially. The reversibility of the dynamics implies that the entropy density of the microstates is conserved in the time evolution. Still, it appears as if equilibrium, with a higher entropy density is approached. In order to understand this process, we solve the dynamics by formally proving how the information-theoretic characteristics of the microstates develop over time. With this approach we can show that an estimate of the entropy density based on finite length statistics within microstates converges to the equilibrium entropy density. The process behind this apparent entropy increase is a dissipation of correlation information over increasing distances. It is shown that the average information-theoretic correlation length increases linearly in time, being equivalent to a corresponding increase in excess entropy.

Ising model

Non-equilibrium

Excess entropy

Q2R

Microscopic reversibility

Information theory

Entropy

Författare

Kristian Lindgren

Chalmers, Energi och miljö, Fysisk resursteori

E. Olbrich

Max-Planck-Gesellschaft

Journal of Statistical Physics

0022-4715 (ISSN) 1572-9613 (eISSN)

Vol. 168 4 919-935

Fundament

Grundläggande vetenskaper

Ämneskategorier

Den kondenserade materiens fysik

DOI

10.1007/s10955-017-1833-8

Mer information

Senast uppdaterat

2018-02-21