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.

中文翻译：

---

细菌种群动态中的信息几何

近年来，研究人员深入研究了信息与随机热力学之间的关系。在本文中，我们应用信息几何来发现细菌生长的物理限制。通过将分布的演变映射到超球面上的运动，我们发现了细菌生长过程中进化时间与成本之间的关系。通过适应性的变化，我们可以了解自然选择如何影响这种关系。从最大熵（MaxEnt）模型中测地线的表达，我们发现细菌生长速率的两个稳态分布之间的统计距离与独立通量的数量成正相关。