  The relationships between reversible Carnot cycles, the absence of perpetual
motion machines and the existence of a non-decreasing, globally unique entropy
function forms the starting point of many textbook presentations of the
foundations of thermodynamics. However, the thermal fluctuation phenomena
associated with statistical mechanics has been argued to restrict the domain of
validity of this basis of the second law of thermodynamics. Here we demonstrate
that fluctuation phenomena can be incorporated into the traditional
presentation, extending, rather than restricting, the domain of validity of the
phenomenologically motivated second law. Consistency conditions lead to
constraints upon the possible spectrum of thermal fluctuations. In a special
case this uniquely selects the Gibbs canonical distribution and more generally
incorporates the Tsallis distributions. No particular model of microscopic
dynamics need be assumed.
