标题： 热系统中自组织现象的信息理论 显示英文标题

标题： The Information Theory of Self-Organization Phenomena in Thermal Systems

摘要： 本文从信息论的角度重新审视布朗运动，旨在探索信息论、热力学和复杂科学之间的联系。 首先，我们提出一个单粒子离散布朗运动模型（SPBM）。在最大熵原理和贝叶斯推断的框架下，我们证明了先验信息与约束条件的等价性，揭示了局部随机性与全局概率分布之间的关系。 通过分析粒子运动，我们发现局部约束和随机性可以导致全局概率分布，从而反映了信息传递过程中局部与全局动力学之间的相互作用。 接下来，我们将研究扩展到多粒子系统，引入“能量作为编码”和“信息温度”的概念，阐明能量分布如何决定信息结构。 我们探讨了能量不仅作为物理系统中的基本物理量，而且本质上是一种信息量，直接决定了系统状态的先验概率分布，从而作为一种信息编码形式。 基于此，我们引入“平衡流”的概念，以解释在能量约束和负信息温度下系统的自组织行为。 通过证明关于平衡流系统的三个定理，我们揭示了自组织的关键性、能量-信息转换效率以及事件发生概率遵循费米-狄拉克分布的特性。 通过理论分析和定理证明，我们为理解复杂系统的动力学提供了新的视角，丰富了信息论、热力学和复杂科学的理论框架，并为相关领域的进一步研究提供了新的理论基础。 显示英文摘要

摘要： This paper revisits Brownian motion from the perspective of Information Theory, aiming to explore the connections between Information Theory, Thermodynamics, and Complex Science. First, we propose a single-particle discrete Brownian motion model (SPBM). Within the framework of the maximum entropy principle and Bayesian inference, we demonstrate the equivalence of prior information and constraint conditions, revealing the relationship between local randomness and global probability distribution. By analyzing particle motion, we find that local constraints and randomness can lead to global probability distributions, thereby reflecting the interplay between local and global dynamics in the process of information transfer. Next, we extend our research to multi-particle systems, introducing the concepts of "Energy as Encoding" and "Information Temperature" to clarify how energy distribution determines information structure. We explore how energy, as not only a fundamental physical quantity in physical systems but also an inherently informational one, directly dictates the prior probability distribution of system states, thus serving as a form of information encoding. Based on this, we introduce the concept of "Equilibrium Flow" to explain the self-organizing behavior of systems under energy constraints and Negative Information Temperature. By proving three theorems regarding Equilibrium Flow systems, we reveal the criticality of Self-Organization, energy-information conversion efficiency, and the characteristic that event occurrence probabilities follow the Fermi-Dirac distribution. Through theoretical analysis and theorem proofs, we offer new perspectives for understanding the dynamics of Complex Systems, enriching the theoretical framework of Information Theory, Thermodynamics, and Complex Science, and providing a new theoretical basis for further research in related fields.