Superconductivity Is Bounded: A Universal Critical Temperature Ceiling from Spectral Dissipation

This paper establishes a universal, law-level upper bound on superconducting critical temperatures based on spectral dissipation constraints. Building on a prior structural result showing that superconductivity corresponds to a dissipationless, closure-protected sector of physical law, we demonstrate that such sectors admit only a finite dissipation budget.

The bound is formulated as an explicit, falsifiable inequality linking the superconducting transition temperature to a measurable normal-state dissipation parameter defined at the Fermi surface. An experimentally grounded proxy based on quasiparticle scattering rates (e.g. ARPES, tunneling, or low-frequency optical measurements) is introduced, enabling direct empirical tests across disparate material classes.

We show that while superconductivity is not forbidden at ambient conditions in principle, its critical temperature is necessarily bounded by universal admissibility constraints independent of microscopic pairing mechanisms. The framework is compatible with BCS, Ginzburg–Landau, and unconventional superconductors, and yields a “Forbidden Zone” in parameter space that excludes arbitrarily high critical temperatures.

The result provides a law-level explanation for the observed saturation of superconducting transition temperatures across materials, and offers a falsifiable criterion that can guide both experimental validation and future materials discovery.

This work is the companion constraint paper to:
A Structural Law of Superconductivity: Dissipationless Coherence from Admissibility and Closure
DOI: 10.5281/zenodo.18136089