Spectral Thermodynamics and the Quantum Arrow of Time
Spectral Thermodynamics and the Quantum Arrow of Time
This paper presents a complete, self-contained mathematical and physical resolution of the Arrow of Time problem. It shows how irreversible thermodynamics, entropy growth, and the observed direction of time emerge from fundamentally time-symmetric quantum and gravitational laws using a spectral thermodynamic framework. The work unifies the quantum, thermodynamic, and cosmological arrows of time through a canonical bridge construction that preserves unitarity and OS-positivity while producing measurable entropy-monotone functionals. It reproduces the second law, Page-curve behavior, and Hawking/Unruh temperatures directly from first principles without ad-hoc statistical assumptions. The model provides falsifiable predictions for entropy flow and spectral observables and establishes universality across black-hole, cosmological, and laboratory thermodynamic systems. It represents the first fully quantitative, falsifiable, and universal derivation of time’s arrow consistent with quantum gravity and information conservation. Related work: Unconditional Exterior Resolution of the Quantum Information Paradox — DOI 10.5281/zenodo.17540398 A Unified Spectral Framework for Quantum Gravity — DOI 10.5281/zenodo.17538401 Quantum Energy Conditions from Spectral Thermodynamics — DOI 10.5281/zenodo.17548423 Resolution of the Cosmological Constant Problem via Spectral Thermodynamic Invariance — DOI 10.5281/zenodo.17550178 See also: The Tier–Omega Monad: Trans-Recursive Completion of the Everything Equation (DOI: 10.5281/zenodo.17859631), which establishes the unique trans-recursive invariant that terminates all possible meta-law recursion and completes the Everything Equation. This work provides the structural boundary underlying the entire framework developed in the associated papers.
Seeley–DeWitt expansion, bounded geometry, arrow of time, Fejér–Hardy normalization, entropy production, Birman–Kuroda theory, mathematical physics, time symmetry breaking, operator theory, quantum information, Page curve, information conservation, unitarity, quantum field theory, black hole thermodynamics, OS positivity, spectral theory, irreversibility, quantum gravity, quantum thermodynamics, entropy law, statistical mechanics, thermodynamic unification, Herglotz transform, falsifiability, universal closure
Seeley–DeWitt expansion, bounded geometry, arrow of time, Fejér–Hardy normalization, entropy production, Birman–Kuroda theory, mathematical physics, time symmetry breaking, operator theory, quantum information, Page curve, information conservation, unitarity, quantum field theory, black hole thermodynamics, OS positivity, spectral theory, irreversibility, quantum gravity, quantum thermodynamics, entropy law, statistical mechanics, thermodynamic unification, Herglotz transform, falsifiability, universal closure
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