- You must have heard the term detailed balance in the context of Markov chains before.
Yes, I have heard of the term detailed balance in the context of Markov chains. In the context of Markov chains, detailed balance refers to a condition that must be satisfied in order for a given system to be in equilibrium. This condition states that the product of the transition probabilities between any two states in the system must be equal to the product of the reverse transition probabilities between those same two states. This ensures that the system will not tend to move towards one particular state over another, and will instead remain in a state of equilibrium.
- That is not quite correct, let's see. Lets denote the transition probability from state x to state y by p(x → y). Detailed balance holds if there is a probability distribution π(x) over the states such that u(x,y) = π(x)p(x → y) is a symmetric function, hence u(x,y) = u(y,x).
You are correct. My previous explanation was not entirely accurate. Deta