CVM Entropy Algebra

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概要

• 論文の詳細を見る

• A concept of correlation correction factor (CCF) for a cluster is introduced to formulate the entropy in the Cluster Variation Method (CVM). As the cluster size increases, the CCF approaches to unity (from below), or -ln(CCF) decreases to zero. The nature of the approximation in the CVM is explained as neglecting the CCF's (or equating them to unity) for clusters larger than the basic cluster of the formulation. For the 2-D square lattice, a hierarchy of entropies for 2×M ladder-shaped clusters converges to the rigorous entropy as M increases to infinity. The convergence is proved, making use of one conjecture that the decrease of -ln(CCF) to zero as the cluster size increases is monotonic. The proof is extended to the 3-D simple cubic lattice, in which an entropy hierarchy made by 2×M×M square-slab clusters converges to the rigorous entropy. The proof for the 3-D case is done for the first time. These proofs of convergence in 2-D and 3-D hierarchies imply that the similar convergence is expected in the Path Probability Method (PPM) for time-dependent kinetics, and suggest the importance of working with a hierarchy of clusters in the PPM.

• 理論物理学刊行会の論文
• 1994-05-31

著者

• Kikuchi R

  Department Of Materials Science And Engineering U. C. L. A.

• Kikuchi Ryoichi

  Department Of Applied Physics Tohoku University:hughes Research Laboratories Malibu:department Of Ma

• Kikuchi Ryoichi

  Department of Materials Science and Engineering, U. C. L. A.

関連論文

• Magnetic Phase Diagram for the Triangular Ising Lattice
• Adsorption of Statistical Copolymers on Surfaces : A Simulation Based on the Cluster Variational Method
• Variational Principle for Stochastic Processes : Generalization of Path Probability Method
• CVM Entropy Algebra
• Solution of the Controversy in the fcc-Based Phase Diagram
• Quantum Statistics Basis, Thermodynamic Analogies and the Degree of Confidence for Maximum Entropy Restoration and Estimation

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