detailed balance

English

Noun

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

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

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

Translations

a quality of Markov processes

• German: detailliertes Gleichgewicht n, detailed balance
• Hebrew: איזון מפורט m (izún meforát)