This implies that the degeneracy of states grows at a decreasing rate with the energy of states. Now I write the stochastic process of the Markov chain in detailed balance. Detailed balance allows me to ignore the constraints of how different configurations are connected since at any point in time, one would find the same number of elements, 𝑛(𝑞), in a certain energy state 𝜀(𝑞). All states are an arbitrary energy ∆𝜀 apart and can transition between each state with the rates 𝑓 𝑢𝑝 and 𝑓 𝑑𝑜𝑤𝑛 , for reaching a state of higher energy or lower energy, respectively. I can then write for the state with the lowest energy, 𝑞 = 0, and for any other energy through using the Equipartition Theorem: 0 = 𝑓 𝑑𝑜𝑤𝑛 𝑔(0) 𝑛(1) -𝑓 𝑢𝑝 𝑔(1) 𝑛(0) (1a) 0 = 𝑓 𝑑𝑜𝑤𝑛 𝑔(𝑞) 𝑛(𝑞 + 1) + 𝑓 𝑢𝑝 𝑔(𝑞) 𝑛(𝑞 -1) -𝑛(𝑞) (𝑓 𝑑𝑜𝑤𝑛 𝑔(𝑞 -1) + 𝑓 𝑢𝑝 𝑔(𝑞 + 1))