𝜕𝕊 𝑡𝑜𝑡 𝜕𝑡 ≥ 0 (32d) Finally, let me examine the entropy change from a heat transfer between two closed mixtures/reservoirs, subscript ℎ𝑜𝑡 and 𝑐𝑜𝑙𝑑, Eqs. 33a, Eq. 33b, taken from Eq. 31c. As heat can only be transferred from hot to cold reservoirs, the entropy will always increase (Eq. 33c). This fundamental principle is a direct consequence from defining temperature as the state of a photon gas, which will always expand from areas of higher to areas of lower density.