Before revision: Detailed balance in reversible chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics whose reaction rate parameters are appropriately constrained, the constraints being imposed by the network structure of the CRN. We will refer to this property as reaction network 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.
After revision: Detailed balance in reversible chemical reaction networks (CRNs) is a property possessed by certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics have the property of reaction network 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.