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

Where the Second Law becomes address counting Version: 1.3 Concept DOI: 10.5281/zenodo.20045306 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper starts from a correction that matters: relative entropy is not ordinary entropy. It is a modular free-charge. For an address \(w\), the anchored modular charge is \[ Q_w=2\pi D(\rho_w\Vert\omega_w), \] while A7 fixes the completed bundle budget \[ Q_w^{\mathrm{vis}}+Q_w^{\mathrm{hid}}=2\pi. \] Local entropy production is the loss of accessible modular free-charge under a physical access map \(\Phi\): \[ \Pi_\omega(\rho,\Phi) = k_B\left[D(\rho\Vert\omega)-D(\Phi\rho\Vert\Phi\omega)\right] \ge0. \] The inequality is the data-processing theorem read through the QTT access ledger. The global Second Law is then an address-counting theorem. The total QTT entropy of a completed ledger domain is \[ S_{\mathrm{QTT}}^{\mathrm{tot}}(T)=k_BN_{\mathrm{addr}}(T), \] and A2/A3 source--sink accounting gives \[ {dS_{\mathrm{QTT}}^{\mathrm{tot}}\over dT} = k_B{dN_{\mathrm{addr}}\over dT} \ge0. \] Visible entropy need not be monotone under every coarse access; the completed microscopic address ledger is the object carrying the monotonic law. The same per-address modular budget gives the finite local entropy and horizon bounds: \[ 0\le S_{\mathrm{QTT}}^{\mathrm{vis}}(R)\le k_B|R|, \qquad S_H\le k_B{A\over4\widetilde\ell^2}. \] It also gives the Page-envelope statement \[ S_{\mathrm{rad}}^{\mathrm{fine}}(T) \le \min\{S_{\mathrm{em}}(T),S_{\mathrm{rem}}(T)\}. \] The laboratory transport check highlighted in the paper combines the thermal conductance quantum with Johnson noise into a parameter-free product: \[ \left({\partial S_V(0)\over\partial T_{\mathrm{th}}}\right) \left({\kappa\over T_{\mathrm{th}}}\right) = {4\pi^2\over3}{k_B^3\over e^2}. \] The ideal test is a same-device measurement of \(R\), \(\kappa/T_{\mathrm{th}}\), and \(\partial_{T_{\mathrm{th}}}S_V(0)\) on one quantized plateau. What the paper gives the reader: a local Second Law from data processing of anchored modular charge; a global Second Law from the growth of completed address count; a finite local entropy bound without an adjustable UV regulator; the area coefficient \(1/4\) from surface-address counting; a Page envelope and transport checks tied to the same modular-budget ledger.