Master equation approach to reversible and conservative discrete systems
Urbina
F
author
Rica
S
author
2016
English
A master equation approach is applied to a reversible and conservative cellular automaton model (Q2R). The Q2R model is a dynamical variation of the Ising model for ferromagnetism that possesses quite a rich and complex dynamics. The configuration space is composed of a huge number of cycles with exponentially long periods. Following Nicolis and Nicolis [G. Nicolis and C. Nicolis, Phys. Rev. A 38, 427 (1988)], a coarse-graining approach is applied to the time series of the total magnetization, leading to a master equation that governs the macroscopic irreversible dynamics of the Q2R automata. The methodology is replicated for various lattice sizes. In the case of small systems, we show that the master equation leads to a tractable probability transfer matrix of moderate size, which provides a master equation for a coarse-grained probability distribution. The method is validated and some explicit examples are discussed.
WOS:000391019100003
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text
files/686_Urbina+Rica2016.pdf
10.1103/PhysRevE.94.062140
Urbina+Rica2016
Physical Review E
Phys. Rev. E
2016
Amer Physical Soc
continuing
periodical
academic journal
94
6
9 pp
2470-0045