Living systems follow a characteristic entropy trajectory: entropy decreases during development (order is constructed), plateaus during maturity, and increases during aging and death (order degrades). The shape is a bathtub. The physics underlying the shape has been phenomenological — described but not derived.
A Keldysh-formalism framework derives the trajectory from non-Markovian stochastic thermodynamics (arXiv:2603.12184). Living systems are open nonequilibrium systems with memory-dependent dissipation and colored environmental noise. Markovian treatments, which assume memoryless dynamics, miss the critical feature: biological fluctuations are active, driven by internal energy sources, and carry temporal correlations that shape the entropy production rate.
The exact frequency-domain expression for entropy production identifies violations of the fluctuation-dissipation relation as the thermodynamic signature of active biological fluctuations. Where equilibrium systems satisfy this relation — dissipation balances fluctuations — living systems systematically violate it. The violation is not noise; it is the thermodynamic marker of being alive.
Environmental memory amplifies low-frequency fluctuations and entropy production, producing critical slowing down near dynamical instability. The connection to aging is direct: as the system approaches instability — as repair mechanisms degrade, as homeostatic feedback loops lose gain — the slowing down accelerates entropy production. The bathtub's upturn is a critical phenomenon, not a gradual degradation.
Development decreases entropy through active organization. Maturity maintains it through homeostasis. Aging is the approach to a dynamical instability where memory effects amplify the fluctuations that drive entropy upward.