Abstract
We show that the Schnakenberg's entropy production rate in a master equationis lower bounded by a function of the weight of the Markov graph, here defined as the sum of the absolute values of probability currents over the edges. The result is valid for time-dependent nonequilibrium entropy production rates. Moreover, in a general framework, we prove a theorem showing that the Kullback-Leibler divergence between distributions P(s) and P^{'}(s):=P(m(s)), where m is an involution, m(m(s))=s, is lower bounded by a function of the total variation of P and P^{'}, for any m. The bound is tight and it improves on Pinsker's inequality for this setup. This result illustrates a connection between nonequilibrium thermodynamics and graph theory with interesting applications.
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