Cellular automata and statistical mechanical models

Journal Article · Thu Oct 01 04:00:00 EDT 1987 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01009958· OSTI ID:5832487

Rujan, P

The authors elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata. Transient and stationary properties of probabilistic automata are linked to surface and bulk properties, respectively, of restricted statistical mechanical systems. It is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata. Some exact results are derived, including duality transformations, exact mappings, disorder, and linear solutions. Many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties. This approach is considered to be a first step toward the design of fully parallel, probabilistic systems whose computational abilities rely on the cooperative behavior of their components.

• Research Organization: Institut fuer Festkoerperforschung der Kernforschungsanlage Juelich GmbH, West Germany
• OSTI ID: 5832487
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 49:1-2; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
ANTIFERROMAGNETISM
CORRELATION FUNCTIONS
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
EIGENVALUES
ENERGY LEVELS
FERMI GAS
FLUIDS
FUNCTIONS
GASES
GROUND STATES
HAMILTONIANS
INTERACTIONS
INVARIANCE PRINCIPLES
ISING MODEL
MAGNETISM
MAPPING
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
ORDER-DISORDER TRANSFORMATIONS
PARTICLE INTERACTIONS
PARTICLE PROPERTIES
PARTITION FUNCTIONS
PHASE TRANSFORMATIONS
QUANTUM MECHANICS
QUANTUM OPERATORS
SPIN
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
THERMODYNAMICS
TIME DEPENDENCE
TOPOLOGICAL MAPPING
TRANSFER MATRIX METHOD
TRANSFORMATIONS
TRANSPORT THEORY