1.Nouna 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
i
j
π
i
=
P
j
i
π
j
{\displaystyle P_{ij}\pi _{i}=P_{ji}\pi _{j}\,}
; where P is the Markov transition matrix and
π
i
{\displaystyle \pi _{i}}
and
π
j
{\displaystyle \pi _{j}}
are the equilibrium probabilities of being in states i and j, respectively."