Meaning
Ground-state Markovization converts an independently certified Dirichlet realization with a strictly positive one-dimensional ground into conservative Markov evolution.
Let H̄h=E₀h with normalized h>0 and ground projection |h⟩⟨h|. Change measure to dν=h²dμ and let U_hf=hf. The transformed nonnegative generator is L=U_h⁻¹(H̄−E₀)U_h, with Markov semigroup e^(−tL). The ground-state equation makes constant functions stationary.
Example (illustrative)
For a symmetric two-state chain, take L=[[1,−1],[−1,1]]. Its ground is the constant vector, its eigenvalues are 0 and 2, and the difference between the two state values decays as e^(−2t). This is a finite illustration of the transformed equilibrium and relaxation floor.
Scope and limits
Subtracting E₀ alone is not the full transform. The Dirichlet realization, positive rank-one ground, and physical comparison bridge are hypotheses; they are not asserted for every vacuum sector.
Source
GAT VIII — Indexed Admissible Distributors and Selected Cofinal Čech Transport in Semisimple Yang–Mills Theory. GAT VIII, Theorem 15.1 context.