The Exclusion Lemma: A Thermodynamic Boundary Between Living Systems and Informational Mimics

This paper introduces the Exclusion Lemma, a minimal thermodynamic condition that distinguishes living systems from non-living informational structures. Rather than defining life through lists of properties such as replication, metabolism, or adaptation, the work reframes the problem in terms of thermodynamic responsibility—whether a system pays, through its own internal coupling, for the continuous re-instantiation of its identity.

The core result is a simple inequality relating informational complexity, execution flux, autonomous energetic intake, and substrate entropy generation. Systems that satisfy this condition are classified as operating in a regime of active coherence, where structure persists through ongoing, internally powered reconstruction. Systems that fail the condition fall into sub-coherence, where informational structure may exist, but persistence depends entirely on external energetic support.

A short contrapositive proof establishes the lemma, followed by concrete applications across three key cases: viruses, dormant genetic material, and contemporary artificial intelligence systems. In each case, the framework provides a principled classification without relying on ambiguous or shifting definitions of life.

The contribution is not a redefinition of life, but a measurement program. By grounding the distinction in quantities that are, in principle, operationally accessible, the Exclusion Lemma shifts the discussion from philosophical debate to empirical evaluation. It asks a precise question of any system: to what extent does it sustain its own existence through autonomous energetic coupling?

This work situates the lemma within existing literature on non-equilibrium thermodynamics, autopoiesis, dissipative structures, and artificial agency, while offering a sharper, testable boundary between systems that instantiate identity and those that merely simulate or depend on it.