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 indirect 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 deviation 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.