Topological Thermodynamics: A Complete Reconstruction from Global Realism, Finite Topological Matter, and Historical Disturbance Fields

Abstract

We reconstruct thermodynamics as a derived physical theory rather than a collection of independent macroscopic postulates. The construction contains exactly three physical axioms in their final unified form: microscopic ontic definiteness and finite localization, physical reality of the spacetime-vacuum substrate, and persistent causal source–response coupling. Every former auxiliary thermodynamic or constitutive postulate is converted into a theorem derived from these axioms together with explicit mathematical admissibility conditions or a controlled scale limit. No fourth physical primitive is introduced. The complete thermodynamic state contains finite topological sectors, probability measures over microscopic histories, and resolved or eliminated historical disturbance variables. The zeroth law follows from constrained entropy maximization; the first law from exact conservation of complete matter–substrate distortion energy; the second law from positive reduced dissipation and information transfer into unresolved histories; and the third law from the spectrum, degeneracy, and accessibility of the minimum-energy topological sector. Heat becomes a declared mode of energy transfer, entropy the measure of unresolved admissible microscopic and historical multiplicity, temperature and chemical potential the conjugates generated by the entropy representation, and irreversibility the lawful dynamics of a reduced matter–memory state. From this foundation we derive corrected ensembles, finite and nonadditive thermodynamics, causal transport, reaction thermodynamics, phase transitions, interfaces, nucleation, glasses, aging, engines, open systems, and driven steady states. Finite-source thermal and virial benchmarks, dense-fluid correlations, mixture structure, and dynamic scattering end in covariance-controlled zero-refit tests. The same energy, entropy, and no-double-counting structure is extended to molecules, polymers, gels, crystals, magnetic and electronic matter, dielectrics, quantum gases, superfluids, superconductors, plasmas, relativistic matter, compact stars, horizons, radiation, gravitation, and information thermodynamics. Classical thermodynamics is recovered as the topology-frozen, memory-eliminated, short-nonlocality limit of this theory. It remains correct on its proper domain but is no longer fundamental or universally complete. The resulting framework replaces separated phenomenological principles by one ordered derivation from structured matter, causal substrate response, and controlled coarse graining, while terminating its new predictions in independently calibrated observables and explicit rejection criteria. **Keywords** Global realism; topological thermodynamics; historical disturbance field; spacetime-vacuum substrate; causal memory; statistical mechanics; nonequilibrium thermodynamics; entropy; thermodynamic laws; finite topological matter; nonadditive systems; zero-refit prediction.