For observables with φ(Γ†)φ(Γ) ≤ 0, the variance obeys Var[φ]/⟨φ⟩² ≥ 1/e^{f(⟨σ⟩)}, where f is the inverse of s tanh(s/2).
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Thermodynamic uncertainty relation for generalized time-reversal observables
For observables with φ(Γ†)φ(Γ) ≤ 0, the variance obeys Var[φ]/⟨φ⟩² ≥ 1/e^{f(⟨σ⟩)}, where f is the inverse of s tanh(s/2).