On the Philosophical Foundation of Mesoscopic Information Theory (v.2.0)
Gang Liu
Classical information theory and quantum information theory are respectively based on Boolean algebra and Hilbert space projection lattices, lacking a unified logical framework for cross-scale physical propositions covering classical, mesoscopic and quantum domains. Traditional physics attributes the classical-quantum transition to continuous spatial scale variation, which is essentially external parameter determinism and cannot explain the peculiar intermediate characteristics of mesoscopic systems. This paper constructs the philosophical and mathematical foundation of mesoscopic information theory based on the coupling of S4 modal logic and the non-distributive modular lattice M₃. A composite axiom system is proposed, and Axiom 3 (a–g) realizes the consistent embedding of S4 modal operators on non-distributive lattices. The cross-scale evolution of physical systems is reinterpreted as discrete phase transition of propositional lattice types, with an endogenous CHSH-type correlation threshold τ≈2.414 serving as the operational criterion for mesoscopic phase. A Möbius-weighted lattice entropy independent of Shannon and von Neumann entropy is established to characterize structural information of mesoscopic logical systems. Noise and decoherence are redefined as intrinsic signals of lattice structural transition rather than simple information dissipation. This study establishes the independent ontological status of mesoscopic propositional systems, breaks the scale-phenomenological paradigm in traditional cross-scale physics, and provides a new foundational framework for the unification of cross-scale information theory.
•Sep 19, 2026•0 citations