TUR (Barato-Seifert 2015): for any steady-state current J, its relative noise satisfies D·J² / ⟨J⟩² ≥ 1/σ. Precision costs entropy: Q = Var(J)/⟨J⟩² · Ṡ ≥ 2k_B. Explore with a driven 3-state Markov chain.
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TUR ratio Q = Var(J)/⟨J⟩² · Ṡ/k_B = —
(must be ≥ 2 by TUR; equality at unicyclic, no leak)