Can Anything from Noether’s Theorem Be Salvaged for Discrete Dynamical Systems?
- Silvio CapobiancoAffiliated withInst. of Cybernetics at TUT
- , Tommaso ToffoliAffiliated withECE Dept., Boston Univ.
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
- Can Anything from Noether’s Theorem Be Salvaged for Discrete Dynamical Systems?
- Book Title
- Unconventional Computation
- Book Subtitle
- 10th International Conference, UC 2011, Turku, Finland, June 6-10, 2011. Proceedings
- pp 77-88
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- analytical mechanics of cellular automata
- second-order dynamics
- energy conservation
- energy as generator of the dynamics
- Noether’s theorem in the discrete
- Industry Sectors
- eBook Packages
- Editor Affiliations
- 16. Department of Computer Science, Science Centre, The University of Auckland
- 17. Department of Mathematics, University of Turku
- 18. Department of Information Technologies, Åbo Akademi University
- 19. Leiden Institute of Center Advanced Computer Science (LIACS), Leiden University
- Author Affiliations
- 20. Inst. of Cybernetics at TUT, Tallinn, Estonia
- 21. ECE Dept., Boston Univ., Boston, USA, MA
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