# detailed balance

## English

### Noun

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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.