Maximum power from a cycling working fluid

We consider the problem of obtaining maximum work from an arbitrary two degree of freedom working fluid coupled to a periodic source of pumped thermal energy f (t). The working fluid is also coupled to a heat bath of temperature T^ex(t) by a conductor of conductance K. We assume that f (t) and T^ex(t) are given functions of time which are piecewise continuous but are otherwise arbitrary. For periodic f (t) and T^ex(t) we find that the available power is given by the variance of f+KT^ex over the period. Even with f 0, the result is interesting. It reduces to the Curzon-Ahlborn⁷ power for step function T^ex(t). It also provides a measure of the power available from temperature fluctuations of the atmosphere.