Visual entropy production estimator of stochastic thermodynamics and application to cyclic population

We propose a visualization method for estimating the entropy production(EP) based on stochastic thermodynamics without prior knowledge of the equation of motion. The entropy production of stochastic thermodynamics is summarized into several observable measurements. Given a time series of observations of a single trajectory, the entropy production in nonequilibrium steady states can be estimated. In numerical simulations of the Lotka–Volterra model, large entropy production is usually accompanied by large environmental forces, which will dominate the population growth. The same conclusion can be drawn from the entropy production of hare-lynx and the ancient Chinese population.