Can anything from Noether's theorem be salvaged for discrete dynamical systems?
Cellular Automata and Lattice Gases
2011-04-05 v2
Abstract
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.
Cite
@article{arxiv.1103.4785,
title = {Can anything from Noether's theorem be salvaged for discrete dynamical systems?},
author = {Silvio Capobianco and Tommaso Toffoli},
journal= {arXiv preprint arXiv:1103.4785},
year = {2011}
}
Comments
6 pages, 2 columns per page. 1 figure. UC2011 conference