Lower bound for entropy production rate in stochastic systems far from equilibrium

We show that the Schnakenberg's entropy production rate in a master equation is 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.

Automated summary

We demonstrate that Schnakenberg's entropy production rate in a master equation can be lower bounded by a function of the weight of the Markov graph. This result is applicable to time-dependent nonequilibrium entropy production rates. Additionally, we prove a theorem in a general framework showing that the Kullback-Leibler divergence between distributions P(s) and P'(s) := P(m(s)) is also lower bounded by a function of the total variation of P and P', for any m. This finding highlights the connection between nonequilibrium thermodynamics and graph theory, and its potential applications.