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  Proof of detailed balance

+ 1 like - 0 dislike

Let's imagine that we have a Lindblad equation. Using that we can derive a Pauli master equation (rate equation) in form like this one (for the stationary case) \[\sum_\limits{k} (w_{nk}P_k - w_{kn}P_n)=0, \\\]

here \(w_{nk} \)is a probability of transition from state n to state k. Detailed balance condition looks like \[w_{nk}P_k = w_{kn}P_n, \,\, \forall n, k.\]Unfortunately, I am not good with this topic. So, I'd like to know if there are any typical ways how to proof that detailed balance condition is satisfied in the system according to the Lindblad equation. 

P.S. In addition we know, that the density matrix is non-diagonal and our distribution is nonequilibrium. 

asked Jun 18, 2020 in Theoretical Physics by MightyPower (10 points) [ revision history ]
recategorized Jun 19, 2020 by Dilaton

Did you look at the literature on this topic? What is it that you cannot comprehend?

In a non stationary (no equlibrium) process there is no a detailed ballance.

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