Fixed Transition probability matrix across nnnp∗(x′) = ∑xT(x′∣x) p∗(x).p^{\ast}(x') \;=\; \sum_{x} T(x' \mid x)\,p^{\ast}(x).p∗(x′)=∑xT(x′∣x)p∗(x).Detailed balanceT(x′∣x) p∗(x) = T(x∣x′) p∗(x′)T(x' \mid x)\,p^{*}(x) \;=\; T(x \mid x')\,p^{*}(x')T(x′∣x)p∗(x)=T(x∣x′)p∗(x′)A Markov chain that satisfies the detailed balance is said to be reversible.