Published June 3, 2026 | Version v1

GLOBAL EINSTEIN -AND- VAN CONG RELATIONS, AND NEW OPTICAL-ELECRICAL-THERMOELECTRIC LAWS IN N(P)-TYPE DEGENERATE, COMPENSATED AND VISCOUS InSb(1-x)P(x)-CRYSTALLINE ALLOY, ENHANCED BY OUR STATIC DIELECTRIC CONSTANT LAW, CONDUCTIVITY MODEL, AND ESPECIALLY ACCURATE FERMI ENERGY EXPRESSION (37)

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In degenerate, compensated and viscous - crystalline alloy, , the Global Einstein -and- Van Cong relations, as those given in Equations (24, 31), and various optical-electrical-thermoelectric laws, enhanced by: the optico-electrical phenomenon (O-EP) and the electro-optical phenomenon (E-OP), as those defined in Eq. (15), our static dielectric constant law given in Equations (1a, 1b), our conductivity model in Eq. (18), and especially our accurate Fermi energy expression in Eq. (11), are now investigated, by basing on the same physical model and the mathematical treatment method, as those used in our recent works.[1,5] Their numerical results are obtained and given in Tables (3-13), suggesting an equivalence between degeneracy-compensation-viscosity concept, given in this X(x)- crystalline alloy. Here, the well-known “local” Einstein relation, being valid only at the lowest degeneracy, lowest viscosity and lowest  compensation, is now globalized by our “Global” Einstein -and- Van Cong relations, valid at any degeneracy, viscosity and compensation, as showed in Equations (24, 31).

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