What have electrons, black holes and Clifford Algebra ever done for us?

  As we know , de Sitter spacetime is a one-parameter thermodynamic system : every state variable is a power of the single horizon radius $l_\Lambda$. This has profound consequences for thermodynamics, information theory, and quantum chaos.     Key results: Smarr relation: $M = (D-1)TS$ (exact for all $D \geq 3$) First law: $dM = (D-2)T dS$ (exact for all $D$) Extended first law $dM = TdS + VdP$ fails except at $D=4$ (numerical coincidence) Pressure ratio: $|\Delta P|/|P_{vac}| = 2/D$ (exact) Ruppeiner metric: $g^{Rupp}_{VV} > 0$ (1D state-space curvature, not stability) Heat capacity: $C_P = -(D-1)S < 0$ (thermal instability) Classical fidelity: $F = 2/(D+1) \approx 2/D$ (asymptotic) Elastic analogy for $D=3$ explains why extended first law fails All results follow from one scale: $\kappa = 1/l_\Lambda$ 1. Setup and Natural Units Converting to SI Units When restoring physical constants: $$\begin{align} S &= \frac{k_B A c^3}{4 G \hbar}\ T &= \frac{\h...