Solar Cell Efficiency Bounds: A Formal Framework for Thermodynamic Limits and Improvement Strategies

We present a formally verified mathematical framework for solar cell efficiency bounds. Starting from the second law of thermodynamics, we derive the Carnot limit η ≤ 1 − T_cell/T_sun and prove that practical efficiency is bounded below unity. We establish a multiplicative loss decomposition where total efficiency factors into absorption, thermalization, and emission components, each constrained to [0,1]. The framework proves multi-junction dominance: adding spectral bands strictly increases efficiency when they capture photons. For concentrator systems, we show that voltage scales logarithmically with concentration factor, V_oc(C) = V_oc(1) + (kT/q)ln(C). Finally, we prove the Gap Theorem: the difference between Carnot and achieved efficiency equals the sum of all loss channels, implying that reducing any loss directly improves efficiency. The formalization comprises 19 verified theorems built on 29 physical axioms in the Platonic kernel.