Paper IV: A Compact U(1)_T Gauge Formulation of Thermodynamics

We formulate an effective compact Abelian U(1)_T gauge sector in which entropy is the conserved charge and k_B is the elementary charge unit. With the Planck-scale normalization ε_t = k_B²/(4πℏ c), μ_t = 4πℏ/(k_B² c), the thermal fine-structure constant is α_T = 1 and the reduced thermal flux is Φ̄_T = ℏ/k_B. The construction gives a four-potential Σ^μ, field tensor Θμν, thermal Maxwell equations, a stress tensor, and a Lorentz-force analogue from a variational principle. Covariance of Σ^μ is stated through a rest-frame decomposition. On an expanding S³ background with R(t) = ct, covariant conservation of the entropy current is compatible with global entropy growth when the associated effective fluid has w_S = –1/3. The paper also records experimental signatures and parameter estimates: entropy-sector wave solutions, thermal Aharonov–Bohm and Josephson effects, a London-scale estimate in superfluid ⁴He under stated assumptions, compact monopole sectors, and a Planck-scale Schwinger-type threshold.