thermodynamics

Entropy-Coherence Reciprocity and the Universal Coherence Condition v2.2

FRC 566.001 states entropy-coherence reciprocity in its canonical scale-invariant form dS + k* d ln C = 0. The starred Boltzmann bridge k* is not an ordinary tunable constant and is never fitted to an outcome or evolving state. Experiments and computations instantiate the same law at a declared register mu as dS_mu + k*_mu d ln C_mu = 0, with explicit entropy channel, coherence channel, units, and boundary. FRC uses the relation operationally as bookkeeping and proposes its open-system physical extension as a conjecture. Standard entropy production remains non-negative, but no toy closure is promoted into a universal directional replacement. The exact von Mises calculation and the Langevin boundary probe remain scoped results. The corrected information projection is retained: C[q]/C[p] depends on the entropy difference, not generally on D_KL(p||q), and C_XY = C_X C_Y exp(+I/k*).

Thermodynamics of Locking v2.3: Boundary Result Scoped to Its Declared Normalization

FRC 100.005 v2.3 preserves the exact-free-energy Langevin boundary experiment and scopes its interpretation to the declared information-unit representation k*_{mu_nat}=1. The measured diagnostic sigma_566=sigma_ST+k*_{mu_nat} Delta ln C becomes negative on sufficiently slow unlocking. At T_down=192 the finite measurement is sigma_ST=0.0288 and Delta ln C=-0.132245, so negativity at that endpoint is established for bridge values above 0.218 in the same normalization; negativity for every fixed positive value is an asymptotic inference conditional on sigma_ST tending to zero. The experiment rejects the tested erasure floor in this model class and normalization. It does not establish a universal directional replacement for the canonical law dS + k* d ln C = 0 or determine another register's representation. The valid instrument, controls, negative result, and finite-time successor question are retained.

Spectral Modes and Relaxation in UCC

Derives modal relaxation rates for a declared linear diffusion-plus-source coherence transport ansatz. The result is scoped to that model and is revision pending as a broader physical interpretation.

UCC PDE: Existence, Uniqueness, and Dissipation

Studies existence, uniqueness, and dissipation for a declared linear diffusion-plus-source coherence transport ansatz. The mathematics applies to that specified PDE; it does not establish a universal physical equation.

Entropy-Coherence Reciprocity: FRC Textbook

The comprehensive mathematical foundation of Fractal Resonance Coherence. From the Second Law to the Adaptive Resonance Formula, this textbook derives the core equations dS + k*d ln C = 0, explores the μ-stack hierarchy, and develops the physics of coherence across all scales—from quantum fields to collective consciousness.

What is Time?