Can Anything from Noether’s Theorem Be Salvaged for Discrete Dynamical Systems?
- Cite this paper as:
- Capobianco S., Toffoli T. (2011) Can Anything from Noether’s Theorem Be Salvaged for Discrete Dynamical Systems?. In: Calude C.S., Kari J., Petre I., Rozenberg G. (eds) Unconventional Computation. UC 2011. Lecture Notes in Computer Science, vol 6714. Springer, Berlin, Heidelberg
The dynamics of a physical system is linked to its phase-space 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.
Keywordsanalytical mechanics of cellular automata second-order dynamics energy conservation energy as generator of the dynamics Noether’s theorem in the discrete
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