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Tag: statistical thermodynamics

The 1-D Cluster Variation Method (CVM) – Simple Application

The 1-D Cluster Variation Method (CVM) – Simple Application

The 1-D Cluster Variation Method – Application to Text Mining and Data Mining There are three particularly good reasons for us to look at the Cluster Variation Method (CVM) as an alternative means of understanding the information in a system: The CVM captures local pattern distributions (for an equilibrium state), When the system is made up of equal numbers of units in each of two states, and the enthalpy for each state is the same (the simple unit activation energy…

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Visualizing Variables with the 2-D Cluster Variation Method

Visualizing Variables with the 2-D Cluster Variation Method

Cluster Variation Method – 2-D Case – Configuration Variables, Entropy and Free Energy Following the previous blog on the 1-D Cluster Variation Method, I illustrate here a micro-ensemble for the 2-D Cluster Variation Method, consisting of the original single zigzag chain of only ten units (see previous post), with three additional layers added, as shown in the following Figure 1. In Figure 1, we again have an equilibrium distribution of fraction variables z(i). Note that, as with the 1-D case,…

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Why Nonadditive Entropy Is Important for Big Data Corpora Combinations

Why Nonadditive Entropy Is Important for Big Data Corpora Combinations

Non-Additive Entropy – A Crucial Predictive Analysis Measure for Data Mining in Multiple Large Data Corpora Statistical mechanics has an important role to play in big data analytics. Up until now, there has been almost no understanding of how statistical mechanics provides both practical value and a theoretic framework for data analysis and even predictive intelligence (sometimes called predictive analysis). In a separate White Paper (link to be provided), I identify – for the first time – how statistical mechanics,…

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Analytic Single-Point Solution for Cluster Variation Method Variables (at x1=x2=0.5)

Analytic Single-Point Solution for Cluster Variation Method Variables (at x1=x2=0.5)

Single-Point Analytic Cluster Variation Method Solution: Solving Set of Three Nonlinear, Coupled Equations The Cluster Variation Method, first introduced by Kikuchi in 1951 (“A theory of cooperative phenomena,” Phys. Rev. 81 (6), 988-1003), provides a means for computing the free energy of a system where the entropy term takes into account distributions of particles into local configurations as well as the distribution into “on/off” binary states. As the equations are more complex, numerical solutions for the cluster variation variables are…

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