On the fast and the slow components of thermal fluctuations

In the framework of extended irreversible thermodynamics, we propose a unified description of the fluctuations of both the temperature and the heat flux. Their two-time correlations are obtained in equilibrium. When applied to non-equilibrium steady states, the formalism suggests some modifications in the usual fluctuation-dissipation expressions, gives a non-vanishing correlation between quantities of different time reversal symmetry, and provides a simple example of the breaking of the validity of the Onsager relations.