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Steady state thermodynamics in population dynamics

We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into housekeeping and excess parts. The housekeeping part represents the integral of stationary growth rate for each condition during a history of the environmental change. The excess part accounts for the excess growth generated when environment is switched. Focusing on the excess growth, we obtain Clausius inequality, which gives the upper bound of the excess growth. The equality is shown to be achieved in quasistatic environmental changes. We also clarify that this bound can be evaluated by "lineage fitness" that is an experimentally observable quantity.