Generalized fluctuation theorems for classical systems

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Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work p(W)/p(-W)=(αW). We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter α becomes a universal parameter 1/kT. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.