2011/09/23 by Norman Margolus, Margolus, Norman
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #cs.IT #math.IT #nlin.CG #quant-ph
paper · pdf · doi:10.48550/arxiv.1109.4995
8 pages, 1 figure
openalex publication_date 2011/09/23 · arxiv created 2011/09/27 · arxiv updated 2011/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical mechanics on a lattice a special case of quantum statistical mechanics, and classical combinatorial entropy a special case of quantum entropy. In a similar manner, finite-state classical dynamics can be recast as finite-energy quantum dynamics. This mapping translates continuous quantities, concepts and machinery of quantum mechanics into a simplified finite-state context in which they have a purely classical and combinatorial interpretation. For example, in this mapping quantum average energy becomes the classical update rate. Interpolation theory and communication theory help explain the truce achieved here between perfect classical determinism and quantum uncertainty, and between discrete and continuous dynamics.