Spalvieri Arnaldo
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy.
Entropy (Basel). 2024 Jan 24;26(2):107. doi: 10.3390/e26020107.
The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is obtained through two approaches: one involves tracing out the environment from a bosonic eigenstate of the combined environment and system of interest (the empirical approach), while the other involves tracing out the environment from the mixed state of the combined environment and system of interest (the Bayesian approach). In the thermodynamic limit, the two coincide and are equal to the multinomial distribution. Furthermore, the paper proposes to identify the physical entropy of the bosonic system with the Shannon entropy of the occupancy numbers, fixing certain contradictions that arise in the classical analysis of thermodynamic entropy. Finally, by leveraging an information-theoretic inequality between the entropy of the multinomial distribution and the entropy of the multivariate hypergeometric distribution, Bayesianism of information theory and empiricism of statistical mechanics are integrated into a common "infomechanical" framework.
本文分析了由任意数量非相互作用玻色子组成的处于平衡态的系统的占据数概率分布和熵。概率分布通过两种方法获得:一种是从感兴趣的环境与系统的组合的玻色子本征态中剔除环境(经验方法),另一种是从感兴趣的环境与系统的组合的混合态中剔除环境(贝叶斯方法)。在热力学极限下,两者一致且等于多项分布。此外,本文提议将玻色子系统的物理熵与占据数的香农熵等同起来,解决了经典热力学熵分析中出现的某些矛盾。最后,通过利用多项分布的熵与多元超几何分布的熵之间的信息论不等式,将信息论的贝叶斯主义和统计力学的经验主义整合到一个共同的“信息力学”框架中。