Entropy-Extended Agam Operator: Quantum Thermodynamic Simulation Code

We introduce the Entropy-Extended Agam Operator ÂΘ, a non-Hermitian generator of quantum evolution on the extended Hilbert space H ⊗ L2 (ℝS), incorporating entropy gradients and memory effects. This operator unifies coherent quantum dynamics, dissipative evolution, and entropic feedback through the inclusion of entropy-dependent potentials and non-Markovian memory kernels. We derive a generalized Schrödinger equation governing the state Ψ(S,t), along with a measurement formalism predicting observable spectra. Experimental validation is presented across physical and biological domains, including spectral shifts in salt-induced combustion and light-evoked biophoton emission in neural tissue. Numerical simulations reveal spectral eigenvalue trajectories λn(t) under entropic coupling. Furthermore, we formulate the Subarna Equation, linking measurable spectra to entropy-modulated coherence, enabling prediction of biological and physical signal dynamics. Together, ÂΘ and the Subarna Equation provide a universal framework for entropy–coherence coupling with implications for quantum thermodynamics, biophysics, and consciousness-related information processing. .