I now define temperature as the density of the surrounding photon gas, where at 𝑇 = 0 K no photons exist and 𝑓 𝑢𝑝 = 0 and we would find all elements at 𝑛(0), equivalent to the third law of thermodynamics. At 𝑇 = ∞, an infinitely dense photon gas, 𝑓 𝑢𝑝 must equal 𝑓 𝑑𝑜𝑤𝑛 , as otherwise the number of elements would not be finite. With the two boundary conditions, I find that 𝑓 𝑢𝑝 must have the form in Eq. 3a with the constant 𝑎. I define the probability density to find an individual element at a state as 𝑝(𝑞) = 𝑛(𝑞) /𝑁, where 𝑁 is the total number of elements of that system. With the definition of the energy levels (Eq. 3b), I can rewrite Eq. 2 and obtain Eq. 3c.