Can anything from Noether's theorem be salvaged for discrete dynamical systems?

Details Can anything from Noether's theorem be salvaged for discrete dynamical systems? Can anything from Noether's theorem be salvaged for discrete dynamical systems?

2011-03-24

arxiv.org/abs/1103.4785v2

Nonlinear Sciences

Cellular Automata and Lattice Gases

6 pages, 2 columns per page. 1 figure. UC2011 conference

Scientific paper

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.

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