Living systems are open nonequilibrium systems that continuously exchange energy, matter, and information with their environments, leading to stochastic dynamics with memory and active fluctuations. In this study, we derive a microscopic non-Markovian description of entropy dynamics in living systems using the Keldysh functional formalism, providing a quantitative foundation for the entropy bathtub picture. The approach naturally incorporates colored environmental noise, memory-dependent dissipation, and many-body interactions, yielding generalized Langevin dynamics and non-Markovian master equations. Within this framework we derive an exact frequency-domain expression for the entropy production rate and show that violations of the fluctuation–dissipation relation provide a direct thermodynamic signature of active biological fluctuations. We further demonstrate that environmental memory enhances low-frequency fluctuations and entropy production, leading to critical slowing down near dynamical instability. These results provide a microscopic physical foundation for the entropy “bathtub’’ picture of living systems and connect entropy evolution with development, aging, and death in nonequilibrium dynamics.
Liu et al. (2026) studied this question.