A local dissipation theorem

The transient time correlation function is a standard method for measuring transport properties in simulations. It represents a special case of a more general theorem, the dissipation theorem, that indirectly calculates phase function averages though the use of the dissipation function. These indi- rect averages often have significantly less statistical error than direct averages. Recently, it has been demonstrated that a local version of the fluctuation theorem can be derived with a well defined devia- tion from the global result at sufficiently low fields. Here we show that a similar local expression can be obtained for the dissipation theorem, providing a way of determining values of phase functions by monitoring the fluctuations of phase functions in a small region of the system.Full Tex