Abstract
In recent years, researchers have delved into the relationship between information and stochastic thermodynamics. In this paper, we apply the information geometry to discover the physical limitation in bacterial growth. By mapping the evolution of distribution to the motion on the hypersphere, we discover a relationship between evolutionary time and cost in the bacterial growth process. Through the change in fitness, we can understand how natural selection affects this relationship. From the expression of geodesic in the maximum entropy (MaxEnt) model, we find that the statistical distance between two steady distributions of bacterial growth rate is positively correlated to the number of independent fluxes.
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