Relation between two proposed fluctuation theorems

Recently van Zon and Cohen [1-3] proposed an extension of the fluctuation theorems (FTs) of Evans and Searles [4]. For dissipative nonequilibrium systems, Cohen and van Zon studied the fluctuations of the heat absorbed Q_t, over a period of time t, by a surrounding thermostat. They showed theoretically that for thermostatted systems their extension does not exhibit the standard form expected for FTs and Pr(βQ_t = -A)/Pr(βQ_t = -A) ≠ exp [A]. In the present paper we show that for thermostatted nonequilibrium steady states modelled by Langevin dynamics, the heat function βQ_t is in fact identical to the time integral of the phase space compression factor βQ_t = A_t which appears in the Gallavotti-Cohen fluctuation theorem (GCFT). Thus the work of van Zon and Cohen confirms at least for Langevin systems, that the GCFT does not apply to thermostatted steady states.