The Ideal Energy of Classical Lattice Dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.

[1]  Tommaso Toffoli,et al.  Cellular Automata as an Alternative to (Rather than an Approximation of) Differential Equations in M , 1984 .

[2]  M. Planck.  Ueber das Gesetz der Energieverteilung im Normalspectrum , 1901 .

[3]  Norman Margolus,et al.  Universal Cellular Automata Based on the Collisions of Soft Spheres , 2008, Collision-Based Computing.

[4]  Anthony J. G. Hey,et al.  Feynman And Computation , 2002 .

[5]  P. Lallemand,et al.  Lattice-gas cellular automata, simple models of complex hydrodynamics , 1998 .

[6]  Norman Margolus,et al.  Physics and Computation , 1987 .

[7]  N. Margolus,et al.  Invertible cellular automata: a review , 1991 .

[8]  N. Margolus.  Mechanical Systems that are both Classical and Quantum , 2008, 0805.3357.

[9]  Norman Margolus,et al.  Quantum emulation of classical dynamics , 2011, ArXiv.

[10]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[11]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[12]  Mark Smith,et al.  Representations of geometrical and topological quantities in cellular automata , 1991 .

[13]  J. Bekenstein.  Universal upper bound on the entropy-to-energy ratio for bounded systems , 1981, Jacob Bekenstein.

[14]  Curious properties of simple random walks , 1993 .

[15]  H. Hrgovčić.  Discrete representations of the n-dimensional wave equation , 1992 .

[16]  Edward Fredkin,et al.  A computing architecture for physics , 2005, CF '05.

[17]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems , 1999, Encyclopedia of Complexity and Systems Science.

[18]  E. Pringsheim,et al.  On the Law of Distribution of Energy in the Normal Spectrum , 2003 .

[19]  J. Kari.  Representation of reversible cellular automata with block permutations , 1996, Mathematical systems theory.

[20]  Cristopher Moore,et al.  New constructions in cellular automata , 2003 .

[21]  Tommaso Toffoli,et al.  Action, or the fungibility of computation , 1999 .

[22]  Stephen Wolfram,et al.  A New Kind of Science , 2003, Artificial Life.

[23]  N. Margolus,et al.  The maximum speed of dynamical evolution , 1997, quant-ph/9710043.

[24]  Jérôme Olivier Durand-Lose,et al.  Representing Reversible Cellular Automata with Reversible Block Cellular Automata , 2001, DM-CCG.

[25]  N. Margolus.  The maximum average rate of state change , 2011 .

[26]  Norman H. Margolus,et al.  Crystalline computation , 1998, comp-gas/9811002.

[27]  Tommaso Toffoli,et al.  Cellular automata machines - a new environment for modeling , 1987, MIT Press series in scientific computation.

[28]  Julia Eichmann,et al.  Lattice Gas Hydrodynamics , 2016 .

[29]  Norman Margolus,et al.  The finite-state character of physical dynamics , 2011, 1109.4994.

[30]  N. Margolus.  Physics-like models of computation☆ , 1984 .