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This paper aims to establish a microscopic foundation for macroscopic phenomenological equations in open systems.

August 11, 2026Open Access

From Binary Randomness to Macroscopic Emergence A Microscopic Derivation of Nonuniformity Emergence, with the Load-Bearing Link Graded in Four Layers

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This paper aims to establish a microscopic foundation for macroscopic phenomenological equations in open systems.
Derivation of macroscopic equations from minimal stochastic axioms and marked extensions.
Verification against stochastic simulations and closed forms when applicable.
Analysis of implications for diffusion coefficients and stability in dynamical systems.
New graded layers for the master equation improved the understanding of macroscopic identity.
Establishment of a one-sided inequality regarding true dissipation in the stock equation.
Identification of quasi-potentials linked to minimized action leading to predictive insights.

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Randomized trial examines the emergence of macroscopic phenomena from microscopic stochastic processes, suggesting new insights into system dynamics.

Qinfu Li (2026) studied this question.

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Randomized trial examines the emergence of macroscopic phenomena from microscopic stochastic processes, suggesting new insights into system dynamics.