Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Coarse-Graining and Master Equation in a Reversible and Conservative System

Discontinuity, Nonlinearity, and Complexity 4(2) (2015) 199--208 | DOI:10.5890/DNC.2015.06.007

Felipe Urbina; Sergio Rica; Enrique Tirapegui

$^{1}$ Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avda. Diagonal las Torres 2640, Peñalolén,Santiago, Chile.

$^{2}$ Departamento de Física, Universidad de Chile, Avda. Blanco Encalada 2002, Santiago, Chile.

Download Full Text PDF

 

Abstract

A coarse graining process is applied to a Ising like model with a conservative and a reversible dynamics. It is shown that, under some assumptions, this coarse graining leads to a tractable probability transfer matrix of finite size which provides a master equation for a coarse graining probability distribution. Some examples are discussed.

References

  1. [1]  Nicolis, G. and Nicolis, C. (1988).Master-equation approach to deterministic chaos, Physical Review A 38, 427-433.
  2. [2]  Nicolis, G., Martinez, S. and Tirapegui, E. (1991). Finite coarse-graining and Chapman-Kolmogorov equation in conservative dynamical systems, Chaos, Solitons and Fractals, 1, 25-37.
  3. [3]  Vichniac, G. (1984), Simulating Physics with Cellular Automata, Physica, D 10, 96-116.
  4. [4]  Pomeau, Y. (1984), Invariant in cellular automata, Journal of Physics A: Mathematical and General , 17 L415-L418.
  5. [5]  Herrmann , H. (1986). Fast algorithm for the simulation of Ising models, Journal of Statistical Physics 45, 145-151.
  6. [6]  Takesue, S (1987). Reversible Cellular Automata and Statistical Mechanics, Physical Review Letters 59, 2499-4503.
  7. [7]  Herrmann, H.J., Carmesin, H.O. and Stauffer, D. (1987). Periods and clusters in Ising cellular automata, Journal of Physics A: Mathematical and General , 20, 4939-4948.
  8. [8]  Goles, E. and Rica, S. (2011), Irreversibility and spontaneous appearance of coherent behavior in reversible systems, The European Physical Journal B, D 62, 127-137.
  9. [9]  Onsager, L. (1944). Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition, Physical Review 65, 117-149.
  10. [10]  Yang, C.N. (1952). The Spontaneous Magnetization of a Two-Dimensional Ising Model, Physical Review 85, 808-816.