2015/05/24 by Siamak Taati, Taati, Siamak
Mathematics · Physics and Astronomy · #37A60 #37B15 #82C03 #Cellular Automata and Lattice Gases (nlin.CG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.DS #math.MP #msc:37A60 #msc:37B15 #msc:82C03 #nlin.CG
paper · pdf · doi:10.48550/arxiv.1505.06464
20 pages, 6 figures
arxiv created 2015/05/24 · arxiv updated 2015/05/27
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal disorder. This chapter is an exposition of this phenomenon and of a statistical scheme for its explanation. The formulation is in the same vein as Boltzmann's ideas, but the simple combinatorial setup offers clarification and hope for generic mathematically rigorous results. Probabilities represent frequencies and subjective interpretations are avoided.