For edge current , the total entropy production rate isIt vanishes precisely when every occupied edge satisfies detailed balance.
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The term "master equation" refers to a mathematical formulation used to describe the time evolution of a system's probabilities over time, particularly in the context of stochastic processes. It's commonly utilized in various fields such as statistical mechanics, quantum mechanics, and chemical kinetics. In general, a master equation provides a way to account for the transitions between different states of a system. The states can represent anything from molecular configurations in a chemical reaction to energy levels of particles in quantum systems.