Regime Transitions Under Finite Power: Stability and Degeneracy in Irreversible Closure Dynamics

Landauer-type bounds constrain the energetic cost of logically irreversible information processing, while finite-power constraints limit sustained operation in finite physical systems. This paper introduces a minimal continuous-time model to explore how these constraints shape long-horizon dynamical transitions between qualitatively different operational regimes. The study identifies three primary fixed points: non-degenerate operation, stall (critical slowing), and trivialization (entropy collapse). Linear stability analysis yields explicit phase-boundary inequalities in terms of dimensionless power-to-cost and depletion parameters. The results provide a structural classification of regime transitions in finite-power irreversible systems within information thermodynamics.