The question of the origin of life long remained at the intersection of chemistry and thermodynamics. Schrödinger's classical idea of "feeding on negative entropy" explains the maintenance of order, but not its emergence. Alongside this work in the archive are studies of the color characteristics of stars suitable for life, quantum models of free will, chaotic switches in living systems, and cellular mechanisms of morphogenesis. All of them, in one way or another, touch on the transition from nonliving to living, but this paper stands out for its attempt to provide a formal physical criterion for the selection of heredity.
The author builds a theoretical model based on large deviation theory and the Crooks fluctuation theorem. Two idealized trajectories of a chemical system are compared: one with simple autocatalysis, the other with an adaptive matrix replicator. For the replicator, an effective adaptation rate α is introduced, which grows linearly with time. Then the integral dissipation is computed for both trajectories and their probability ratio. The key step is the derivation that this ratio grows as a double exponential of time.
The main result is Proposition 1: in a system containing precursors for both a static autocatalyst and an adaptive replicator, the ratio of the probabilities of the replicative trajectory to the autocatalytic one grows as exp(exp(τ²)). This means that for sufficiently long times the replicative trajectory becomes overwhelmingly more probable. The critical takeover time τ(crit) is determined by the moment when the accumulated effect of adaptation compensates for the replicator's initial kinetic lag. Threshold conditions are also formulated: replication accuracy above the Eigen threshold, kinetic rate above the degradation rate, sufficient resource, and protection from parasitic sequences.
The work differs from neighboring studies in that it offers not a qualitative description but a rigorous mathematical criterion for the selection of heredity. Unlike the papers on star color or cellular mechanisms, the focus here is on the thermodynamic basis of evolution. This is the first attempt to derive Darwinian selection as a consequence of the statistical physics of nonequilibrium systems, rather than as a separate biological principle. Such an approach could unite physics and biology in explaining the origin of life.
The model assumes an inexhaustible resource and neglects spatial heterogeneity and compartmentalization. Future work could incorporate coupled differential equations for different species to describe parasite dynamics more accurately. It would also be interesting to study the saturation of the adaptation rate as biochemical limits are approached. An extension to multidimensional fitness landscapes is possible.
The results could influence experimental origin-of-life chemistry by offering a clear quantitative signature of the transition to an evolving system. They also provide a new perspective on dynamic kinetic stability in nonequilibrium thermodynamics.
Conduct the proposed experiment with a flow reactor and isothermal calorimetry to test the predicted signature. Develop a more realistic model accounting for resource depletion and spatial effects.
In the field of the origin of life, the question of how hereditary information arises from nonliving matter remains unresolved. This work links that problem to fundamental principles of statistical physics, proposing a mechanism for the selection of heredity through dissipation. This directly relates to the problem of abiogenesis and the transition from chemical to biological evolution.
The double exponential in the probability means that after the critical moment the replicative trajectory becomes not merely more probable, but so dominant that the logarithm of its logarithm grows quadratically with time. This is one of the fastest growths encountered in physical models.