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

• URL: http://arxiv.org/abs/2604.07641v1
• Date: Wed, 08 Apr 2026 23:01:36 GMT
• Title: A Thermodynamic SU(1,1) Witness Framework for Double-Quantum NMR Signals in Neural Tissue
• Abstract summary: Entanglement criteria based on variances or Fisher information are well developed for compact collective spin algebras.<n>We develop a thermodynamic witness framework in which the classically accessible fluctuation sector is strictly bounded by finite-temperature detailed-balance conditions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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