Nonequilibrium partition identity

The nonequilibrium partition identity (NPI) is a remarkably simple and elegant consequence of the fluctuation theorem previously known as the Kawasaki identity: ⟨ exp ⁡ [ − Σ ¯ t t ] ⟩ = 1 , ∀ t {\displaystyle \left\langle {\exp[-{\overline {\Sigma }}_{t}\;t]}\right\rangle =1,\quad \forall t} (Carberry et al. 2004).