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arXiv · 2503.17898

Matrix approach to generalized ensemble theory for nonequilibrium discrete systems

Shaohua Guan
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Abstract

A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing an observation matrix, we show that any discrete probability distribution can be formulated as a generalized Boltzmann distribution, with observables and their conjugate variables serving as basis vectors and coordinates in a vector space. Within this framework, we identify the minimal sufficient statistics required to infer the Boltzmann distribution. The nonequilibrium thermodynamic relations and fluctuation-dissipation relations naturally emerge from this framework. Our findings provide a new approach to developing generalized ensemble theory for nonequilibrium discrete systems.

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Shaohua Guan. 2025-03-23. Matrix approach to generalized ensemble theory for nonequilibrium discrete systems. https://doi.org/10.1103/xkkn-cw77

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