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:
(Carberry et al. 2004). Thus in spite of the second law inequality which might lead one to expect that the average would decay exponentially with time, the exponential probability ratio given by the FT "exactly" cancels the negative exponential in the average above leading to an average which is unity for all time.
The first derivation of the nonequilibrium partition identity for Hamiltonian systems was by Yamada and Kawasaki in 1967. For thermostatted deterministic systems the first derivation was by Morriss and Evans in 1985.