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.