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 Qt, 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(βQt = -A)/Pr(βQt = -A) ≠ exp [A]. In the present paper we show that for thermostatted nonequilibrium steady states modelled by Langevin dynamics, the heat function βQt is in fact identical to the time integral of the phase space compression factor βQt = At 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