Action, or the fungibility of computation
Feynman and computation
How to turn a second-order cellular automaton into a lattice gas: a new inversion scheme
Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
Methodology and implementation of a software architecture for cellular and lattice-gas automata programming
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The dynamics of a physical system is linked to its phasespace geometry by Noether's theorem, which holds under standard hypotheses including continuity. Does an analogous theorem hold for discrete systems? As a testbed, we take the Ising spin model with both ferromagnetic and antiferromagnetic bonds. We show that-and why-energy not only acts as a generator of the dynamics for this family of systems, but is also conserved when the dynamics is time-invariant.