A Thermodynamic SU(1,1) Witness Framework for Double-Quantum NMR Signals in Neural Tissue

TL;DR

This paper introduces a thermodynamic framework for bounding double-quantum NMR signals in neural tissue, enabling rigorous classification of anomalies as quantum or classical phenomena.

Contribution

It develops a novel thermodynamic witness framework that constrains classical fluctuations in double-quantum NMR, allowing for the identification of quantum effects in neural tissue.

Findings

Transient pair correlations are capped near 10^{-9} amplitude.

Classical coherent sequence amplification is bounded to approximately 10^{-2}.

Macroscopic DQ anomalies of 10-15% can be classified as quantum if structural stability is verified.

Abstract

Entanglement criteria based on variances or Fisher information are well developed for compact collective spin algebras, but their extension to non-compact dynamical sectors is less straightforward. In particular, double-quantum (DQ) observables associated with effective SU(1,1) structures can lead to formally unbounded classical fluctuation estimates unless additional physical constraints are imposed. In this note, we develop a thermodynamic witness framework in which the classically accessible fluctuation sector is strictly bounded by finite-temperature detailed-balance conditions and motionally narrowed sequence-transfer limits. By analyzing the quantum dynamical semigroup of the spin-bath interaction, we demonstrate that spontaneous transient pair correlations generated by a stationary incoherent bath are contractively capped near an amplitude of \(10^{-9}\). Furthermore, classical coherent sequence amplification is empirically bounded to \(\mathcal{O}(10^{-2})\) in motionally narrowed tissue. The resulting functional provides a concrete, theoretically derived bounding framework against which macroscopic DQ anomalies (e.g., fractional amplitudes on the order of \(10\%\) to \(15\%\)) can be rigorously classified as classically inexplicable, provided macro-scale structural stability (constant \(T_2^*\)) is empirically verified.