detailed balance

detailed balance (plural detailed balances)

1. (mathematics, probability theory) a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey

   ${\displaystyle P_{ij}\pi _{i}=P_{ji}\pi _{j}\,}$

   where P is the Markov transition matrix and ${\displaystyle \pi _{i}}$ and ${\displaystyle \pi _{j}}$ are the equilibrium probabilities of being in states i and j, respectively.