已有 5948 次阅读 2013-5-26 16:04 |个人分类:量子干涉|系统分类:论文交流| 元胞自动机, 变值体系, 变值相空间, 量子统计解释, 交互作用模型

- 基于量子模型的统计力学从概率统计测量,微系综到系综矩阵的相互作用模式

   本论文为Intech 2013年5月出版的专著:Emerging Applications of Cellular Automata 中第6章。在这篇论文中系统地描述了如何利用变值相空间体系,对基于量子模型的统计力学特有的相互作用模式,形成从基础的概率统计测量,微系综到系综矩阵描述体系。对不同的相互作用形成了系统的系综矩阵描述模式,提供了一系列可视化分布。




Interactive Maps on Variant Phase Spaces
– From Measurements - Micro Ensembles to Ensemble  Matrices on Statistical Mechanics of Particle Models

This chapter provides a brief investigation into Variant Phase Space (VPS) construction.   Using an n variable 0-1 function and an N bit vector, a VPS hierarchy can be progressively  established via variant measures, multiple or conditional probability measurements, and   selected pair of measurements to determine a Micro Ensemble (ME) and its eight interactive projections.

Collecting all possible $2^N$ pairs of probability measurements, a Canonical  Ensemble (CE) and its eight Interactive Maps (IMs) are generated following a bottom-up approach.

Applying a Maxwell demon mechanism, all possible $2^{2^n}$   functions can be calculated to create a result comprising a {CE} and eight sets of {IM}. Using either a CE or an IM as an element,  it is possible to use a variant logic configuration to organize each set of distributions to be a $2^{2^{n−1}}× 2^{2^{n−1}}$  matrix as a CE Matrix (CEM) or IM Matrix (IMM), respectively. Following a top-down approach, a CEM or IMM can be decomposed into two polarized matrices with each matrix having periodic properties that meet the requirements of a Fourier-like transformation.

The main results are presented as ten propositions and four predictions to provide a foundation for further exploration of quantum interpretations, statistical mechanics, complex dynamic systems, and cellular automata.

The chapter does not explore global properties in detail, and further detailed investigations and expansions are necessary.  

Anticipating that the principles put forward in this chapter will prove to be well founded, we look forward to exploring advanced scientific and technological applications in the near future.

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