Statistical Thermodynamic Foundation for the Origin and Evolution of Life

In this paper we review and extend our earlier recent work on thermostated systems. A description of nano-biological systems by Markov chains in coordinate space in the strongly overdamped limit is presented. Characterization of the most probable path is given and a new formula for the probability of this special path is provided from recursion formulae. The deterministic limit is derived and the significance of Lagrange multipliers introduced when constructing the most probable path is elucidated. The characterization of the generation of path entropy by the most probable path is given an equivalent interpretation relating to the rate of entropy production by the most probable path. The paper concludes with an account of the biological implications. Here we address why the origin of life and its subsequent evolution took place, not the particular chemical details of how it happened.

💡 Research Summary

The paper presents a comprehensive statistical‑thermodynamic framework aimed at explaining why life originated and subsequently evolved, deliberately sidestepping the detailed chemistry of prebiotic reactions. The authors begin by modeling nanoscale biological systems in the strongly overdamped regime as Markov chains defined in coordinate space rather than in reaction‑network space. This choice allows the microscopic degrees of freedom (particle positions, conformational coordinates) to be directly linked to macroscopic thermodynamic quantities such as free energy and entropy production. By employing the overdamped limit of the Langevin equation, they derive a Fokker‑Planck description that can be recast as a path‑integral over discrete time steps, laying the groundwork for a probabilistic description of entire trajectories.

The central technical contribution is the rigorous definition of the “most probable path” (MPP). The authors introduce Lagrange multipliers to enforce constraints (e.g., conservation of energy, mass, or other conserved quantities) along a candidate trajectory. Using a recursion relation, they obtain a closed‑form expression for the probability of any discrete path and, in particular, for the MPP. This expression generalizes the classical principle of least action: instead of minimizing an action functional, the MPP maximizes a path‑probability functional that explicitly incorporates stochastic fluctuations. The deterministic limit of the recursion recovers ordinary differential equations, and the Lagrange multipliers acquire a clear physical interpretation as generalized forces (chemical potential gradients, mechanical stresses, etc.).

A novel conceptual bridge is built between the MPP and entropy production. The authors define “path entropy” as the negative logarithm of the path probability and demonstrate that the rate of increase of this quantity along the MPP equals the thermodynamic entropy production rate. In other words, the MPP is the trajectory that maximizes entropy production under the imposed constraints—a statement reminiscent of the Maximum Entropy Production principle but derived here from first‑principles stochastic dynamics. This equivalence provides a quantitative link between information‑theoretic measures (path entropy) and classical non‑equilibrium thermodynamics.

The biological implications are then explored. The early Earth is portrayed as a high‑energy, highly dissipative environment that offered a vast “path space” of possible stochastic trajectories. According to the framework, trajectories that yielded the greatest entropy production were statistically favored, leading to the spontaneous emergence of self‑replicating structures, metabolic cycles, and eventually more complex organization. The authors argue that the driver of biogenesis is not a specific catalytic molecule or a particular reaction pathway, but the universal thermodynamic tendency of dissipative systems to select high‑entropy‑production routes. Evolution, in this view, is a continuation of that selection process: mutations and ecological pressures shift the accessible path space, and those variants that further increase entropy production become dominant.

The paper concludes by acknowledging limitations: the current model assumes strong overdamping, neglects inertial effects, and treats the system in a reduced coordinate space, which may omit important biochemical details. Nevertheless, the authors suggest that coupling this statistical‑thermodynamic scaffold with detailed chemical kinetics could yield a unified theory of life’s origin that bridges non‑equilibrium physics, information theory, and biology. In sum, the work offers a mathematically rigorous, physically transparent, and conceptually bold perspective on why life emerged and how it continues to evolve, positioning entropy production as the fundamental “engine” behind the phenomenon.