Before revision:  Stochastic detailed balance ( SDB)is achieved in Markov chains when the transition rates satisfy certain constraints. We show that if a chemical reaction network modeled with mass-action kinetics possesses DDB, then it also possesses SDB. In order to show that the converse is not true in general, we present examples of networks which have SDB but not DDB.
After revision:  Stochastic detailed balance ( RNDB). Markov chains (whether arising as models of CRNs or otherwise) have their own notion of detailed balance, imposed by the network structure of the graph of the transition matrix of the Markov chain. When considering Markov chains arising from chemical reaction networks with mass-action kinetics possesses DDB, then it also possesses SDB. In order to show that the converse is not true in general, we present examples of networks which have SDB but not DDB.