Viability Boundaries of Living Systems: A Phenomenological Theory (EN)

What distinguishes a living system from a non-living one — not by a list of features, but by a criterion that can actually be computed? Theoretical biology answers this in roughly two ways. Replication-first accounts (the RNA world, the Joyce/NASA working definition) hold that life is that which reproduces and evolves by Darwinian selection. Maintenance-first accounts (Bauer, Rosen, autopoiesis) hold that life is that which actively holds itself away from equilibrium. This work belongs to the second tradition. The replication-first criterion has a known weakness: taken strictly, a mule is not alive, nor is a sterile worker bee, a somatic cell, or a childless person. The capacity to reproduce characterizes the persistence of a lineage, not the life of an individual. The maintenance-first position was stated most sharply by Ervin Bauer (1935): all and only living systems are never in equilibrium and perform, at the expense of their free energy, continuous work against the equilibrium that the laws of physics and chemistry would otherwise impose. Bauer also saw the consequence — the external work a living system performs destroys the very structure that its internal work restores, an irremovable contradiction that ends life once the capacity for internal work is exhausted. He stated this without equations. The present work closes that gap. Its physical core is that repair can be neither perfect nor free: it never returns a system exactly to its prior state, every act of repair leaving an irreversible trace, and it carries a thermodynamic price whose floor is set ultimately by Landauer's principle. The energy available to pay that price is bounded twice over — by physics, and, for each species, by evolution, which tunes the repair budget to reproductive success rather than to longevity. On this footing the finiteness of life ceases to be an empirical generalization and becomes a structural consequence. Formally, the state of a living system is described by four coupled nonlinear ordinary differential equations, each derived from an independent phenomenological principle, governing an integrity potential E (t), an irreversibly accumulated structural entropy Σ (t), an assimilation efficiency ηabs (t) carrying a nonlocal memory of accumulated damage, and a repair reserve R (t). Because death proceeds through E and R alone, the framework can be described compactly as an (E, R) -system with memory. The finiteness of lifetime is proved as a theorem rather than postulated: any trajectory originating above the viability boundary leaves the viability domain within finite time. Two functionally irreducible channels carry it. The integrity-potential channel (E-channel) is unconditional under the model's axioms; the repair-reserve channel (R-channel) — biologically dominant and typically the earlier of the two — operates under an additional condition on accumulated structural entropy, which progressively depresses the repair-reserve attractor below its death threshold. The imperfection of repair is necessary but not sufficient for the proof: what makes finiteness provable is the irreversible, history-dependent memory, in which assimilation efficiency decays with the accumulated integral of structural entropy rather than with its instantaneous value — a nonlocal formulation absent from conventional thermodynamic descriptions. The viability boundary ℳmin is a critical surface in parameter space: the locus at which the attractor of the repair reserve coincides with its bifurcation threshold R*, separating configurations capable of sustaining life from those in which life cannot occur. It resolves into three necessary conditions that must hold jointly — an autocatalytic threshold for repair, a separation of timescales between damage and its export, and a resource threshold for sustaining memory. These are three conditions but two channels: the first guards the repair reserve, the other two guard the integrity potential at different stages. Violation of any single one rules out a viable trajectory and cannot generally be compensated by external conditions. This makes the origin of life a triple threshold rather than a single one, and yields a structural explanation for the rarity of abiogenesis: the probability of a spontaneous transition may scale as the product of three independently small barrier-crossing probabilities. It also suggests a use for experimental programs — diagnosing, for a given candidate system, which barrier remains unsatisfied and what minimal conditions would satisfy it. Which channel closes a given life is species-specific. In most species the repair reserve is exhausted first, and death comes through R while the integrity potential is still high; in some long-lived species, where that depletion is suppressed, death arrives instead through E with the reserve still largely intact. The balance between the two is governed by a single parameter — the sensitivity of the assimilation machinery to accumulated damage. Under stated conditions the analysis locates an optimum at which the dominant channel switches from R to E, with the values calibrated for real species lying below it: evolution settles the repair budget where reproductive success is greatest, not where lifespan is longest. The boundary is given quantitative form through several independent anchors, among them the minimal synthetic cell JCVI-syn3. 0 — the experimentally characterized organism with the smallest known viable genome — and the Landauer limit. A scaling invariant ℬ ≡ (E0 − E*) · τenergy, with the dimension of action (J·s), combines the structural energy budget with a characteristic thermodynamic timescale; its mass-normalized form ℬ* = ℬ/M^ (5/4) is observed to be approximately conserved across the 306 mammalian species examined. Numerical integration of the governing equations reproduces the three phases of the life cycle — growth, plateau, and collapse — without an added assumption; the specific contribution of the theory is that the boundaries between phases are determined analytically through the parameters ν0, ρ, σ0, and α. A systematic table then organizes living and sub-biological structures by memory regime and by position relative to ℳmin. Most cells are populated by known organisms; some are excluded outright by the finiteness theorem; the remaining empty cells constitute falsifiable predictions — classes of structures the theory permits but that have not yet been observed. Examples include syn3. 0, sitting essentially on ℳmin; obligate endosymbionts and organelles, lying below it; and spores and tardigrades in anabiosis, occupying a separate class of pre-boundary states, each further classified by death mechanism and evolutionary fate. On empirical status the work is explicit. Parameters are calibrated against data of independent origin — cross-species telomere shortening rates, the age decline of maximal oxygen consumption — rather than against lifespan itself, and the resulting predictions are consistent with several independent biological datasets. The theory's most distinctive claims, the nonlocal memory mechanism and the two-channel structure of death, are formulated as falsifiable but have not yet received direct empirical test. What is proved, what is calibrated, and what remains hypothetical are marked off separately. The work continues the tradition of Ervin Bauer (1935) and Ilya Prigogine (1977): Bauer's principle of steady disequilibrium and Prigogine's theory of dissipative structures are unified here and extended by a nonlocal memory mechanism — the element that turns the finiteness of life from an empirical observation into a theorem, and yields an explicit mathematical criterion distinguishing living from non-living matter. https: //github. com/vaavdeev/VBLS