  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.
