Phenomenological framework for fluctuations around steady state

A phenomenological framework to describe fluctuations around steady states is formulated. The framework is illustrated for a magnetic system maintained at a nonequilibrium steady state by an oscillating magnetic field, modeled at the mesoscopic level by a Langevin dynamics. The large deviation formalism along the time axis is employed to construct a generalized entropy to describe the fluctuations in the steady state for time averaged observables (state variables). We propose a phenomenological postulate that the fluctuations about the steady state can be obtained from the response of the state variables to "thermodynamic conjugate forces" (fluctuation-response relation), as in the ordinary thermodynamic fluctuation theory. An experimentally realizable method to study the linear response about the steady state against state variable perturbations is proposed, and illustrated for the driven magnetic system. The notion of a proper state space to describe nonequilibrium steady states is discussed, and to this end, we introduce a dissipation variable to extend the state space for our model system. In the extended state space, we elucidate and study various stability and Maxwell-type relations that follow from our local phenomenological (thermodynamic) framework. Some relevant issues regarding a more general thermodynamic framework are also discussed.