The Preisach Extremum Stack is a Shannon-Minimal Sufficient Statistic for Rate-Independent Functionals
Preisach 极值栈是速率无关泛函的 Shannon 最小充分统计量
Let R denote the class of all computable, causal functionals that are rate-independent in the classical sense (invariant under monotone time reparametrizations), and let Pi_n be the Preisach extremum stack of an input sequence u_{0:n}. We prove a characterization theorem establishing that every F in R satisfies Fu = f(Pi_n) for a computable f, and derive two information-theoretic results. First, under any probability measure on u_{0:n}, the equality I(u_{0:n}; Fu) = I(Pi_n;…