Entropy Production as Anchored Modular Charge: A Parameter-Free QTT Derivation of the Second Law and Its Area-Law, Page-Bound and Transport Consequences

The Second Law is usually derived by adding coarse graining, typicality, molecular chaos or a low-entropy initial condition to reversible microscopic dynamics.

Here the arrow is instead obtained as a structural ledger theorem inside Quantum Traction Theory (QTT).

Each Reality-Dimension address w carries a finite, complete modular budget Q_bundle = 2π.

The visible share is measured by the anchored Umegaki-Araki charge Q_w = 2π D(rho_w || omega_w), while entropy production is the irreversible loss of accessible modular charge under admissible dynamics.

Positivity and data processing of relative entropy give local Clausius and fluctuation inequalities.

QTT creation then makes the active address count non-decreasing, so dS_QTT/dT = k_B dN_addr/dT >= 0.

The same budget gives S <= k_B A/(4 ell_tilde^2), a sharpened Page bound S_rad <= min{S_em, S_rem}, an operational quantum-classical decoherence map Gamma = -d_T ln V, and numerically confronted transport checks (Lambda_triad = 1.06 +/- 0.07 from existing electronic quantum-point-contact data, 0.86 sigma from unity).

The result is conditional on the QTT axioms A1/A3/A5/A6/A7, but contains no fitted thermodynamic coefficient. The cross-paper QTT identification ell_tilde = ell_P uses the parameter-free gravitational coupling G = ell_tilde^2 c^3 / hbar derived in the QTT Einstein-Hilbert endurance paper.

Status legend used throughout: S = standard mathematics or established physics; P = QTT postulate; C = QTT consequence conditional on P; E = empirical decision rule.