Thermodynamic Uncertainty Relation

Speed–accuracy–dissipation tradeoff: precise molecular currents require high entropy production

Forward rate k⁺ 2.0 Backward rate k⁻ 0.5 Side rate k_s 1.0 Particles N 500

⟨J⟩: --

Var(J): --

Σ (ent.prod): --

TUR ratio Q: --

TUR bound: Q≥2

TUR (Barato-Seifert 2015): Var(J)/⟨J⟩² ≥ 2kB / σ̇ → Q = σ̇ · Var(J)/⟨J⟩² ≥ 2

Entropy production: σ̇ = Σ_edges J_e · ln(k⁺_e / k⁻_e) [local detailed balance]

Speed-accuracy: fast + precise currents require large dissipation — biological molecular motors

Equality: Q=2 only for unicyclic networks at steady state — all others exceed bound