- 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。

   利用元胞自动机及其动态表示探索量子交互作用是一类新的探寻模式，希望该类模型和方法对于利用概率统计系统模型深入探讨量子力学的基础统计解释能起到积极推进作用。

   对该类前沿探索性论题，欢迎讨论，不足之处敬请批评指正。

  论文全文可从网上免费获取：

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.