Rescaled entropy of cellular automata
arXiv:2005.08585 · doi:10.1088/1361-6544/abfeab
Abstract
For a d-dimensional cellular automaton with d 1 we introduce a rescaled entropy which estimates the growth rate of the entropy at small scales by generalizing previous approaches [1, 9]. We also define a notion of Lyapunov exponent and proves a Ruelle inequality as already established for d = 1 in [16, 15]. Finally we generalize the entropy formula for 1-dimensional permutative cellular automata [18] to the rescaled entropy in higher dimensions. This last result extends recent works [17] of Shinoda and Tsukamoto dealing with the metric mean dimensions of two-dimensional symbolic dynamics.
Some inaccuracies in Section 4 and 5 corrected