Non-Markovian Entropy Dynamics in Living Systems from the Keldysh Formalism

TL;DR

This paper develops a non-Markovian theoretical framework using the Keldysh formalism to analyze entropy dynamics in living systems, capturing memory effects, active fluctuations, and their thermodynamic signatures.

Contribution

It introduces a novel non-Markovian approach to entropy dynamics in living systems, incorporating environmental memory and active fluctuations via the Keldysh formalism.

Findings

Derives an exact frequency-domain expression for entropy production rate.

Shows violations of fluctuation-dissipation relation indicate active biological fluctuations.

Environmental memory increases low-frequency fluctuations and entropy production.

Abstract

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 develop a non-Markovian theoretical framework for the entropy dynamics of living systems based on the Keldysh functional formalism and stochastic thermodynamics. 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.