A Thermodynamic Theory of Learning Part II: Critical Period Closure and Continual Learning Failure

Learning performed over finite time is necessarily irreversible. In Part~I of this series, we modeled learning as a transport process in the space of parameter distributions and derived the Epistemic Speed Limit, which lower-bounds entropy production under finite-time learning. In this work (Part~II), we study the consequences of this irreversibility for continual learning from a trajectory-level perspective. We show that finite dissipation constrains not only which solutions are reachable, but which learning paths remain dynamically accessible. Although a continuum of task-equivalent realizations can achieve identical task performance, finite-time learning irreversibly selects among these realizations. This selection occurs through the progressive elimination of degrees of freedom that would otherwise enable structural reconfiguration. We refer to this phenomenon as \emph{critical period closure}: beyond a certain stage of learning, transitions between compatible representations become dynamically inaccessible under any finite dissipation budget. As a result, continual learning failure arises not from the absence of solutions satisfying multiple tasks, but from an irreversible loss of representational freedom induced by prior learning. This reframes catastrophic forgetting as a dynamical constraint imposed by finite-time dissipation, rather than direct task interference.