Elastic Markov Blanket: A Free-Energy Framework for Dynamic Boundary Stability

抄録

We introduce the Elastic Markov Blanket (EMB), a dynamic and deformable extension of the free-energy principle that formalizes how systems maintain statistical separability under fluctuating environmental conditions. Unlike the conventional static blanket, the EMB allows reversible (shape-memory) deformations represented by a time-varying boundary B(t) ∈ Rm that mediates coupling between internal and external states. The boundary dynamics follow a dual gradient flow minimizing the composite potential V(μ,B) = F(μ,B) + UB(B), where F denotes variational free energy and UB an elastic potential enforcing restoration toward an equilibrium configuration B0. We derive Lyapunov stability conditions for this coupled system, showing that the composite potential decreases monotonically and trajectories converge to an invariant set defined by simultaneous inference and structural equilibrium. The result provides a mathematical account of boundary self-regulation in both biological and artificial agents. This framework completes our Lyapunov-based trilogy, unifying inference, consciousness, and boundary dynamics.