Journal Article

Entropy Bathtub for Living Systems: A Markovian Perspective

Fornalski, Krzysztof W.

2026

Overview

A living organism can be regarded as a dissipative, self-organizing physical system operating far from thermodynamic equilibrium. Such systems can be effectively described within the framework of Markov jump processes subjected to an external driving force that sustains the system away from equilibrium—leading, in the special case of stabilization, to a non-equilibrium steady state (NESS). By combining the Markov formalism with concepts from stochastic thermodynamics, we demonstrate the temporal evolution of entropy in such systems: entropy decreases during growth and development, stabilizes at maturity under NESS conditions, and subsequently increases during aging, death, and decomposition. This characteristic trajectory, which we term the entropy bathtub, highlights the universal thermodynamic structure of living systems. We further show that the system exhibits continuous yet time-dependent positive entropy production, in accordance with fundamental thermodynamic principles. Perturbations of the driving force—whether reversible or irreversible—naturally capture the impact of external stressors, providing a conceptual analogy to pathological processes in biological organisms. Although the model does not introduce fundamentally new elements to the physics of life, it offers a simple tool for exploring entropy-driven mechanisms in living matter.

• Publisher: MDPI AG,Multidisciplinary Digital Publishing Institute (MDPI)
• Subject: Analysis / Biological activity / Entropy / Equilibrium / Homeostasis / living systems / Markov / Markov processes / non-equilibrium steady state / physics of life / Probability distribution / Statistical physics / stochastic thermodynamics / Thermodynamic equilibrium / Thermodynamics