Fluctuation dissipation theorems are derived for thermodynamic properties like frequency dependent specific heat and compressibility. First the case where a systems dynamics are restricted by constant volume and energy is considered. The dynamic linear response to a heat pulse and a volume change at time zero is calculated, under assumption of energy conservation. Then the case of isothermal isobaric conditions are treated by a slight modification of ordinary linear response theory. In both cases the perturbation cannot be stated through the Hamiltonian, but has to be imposed by variation of the external thermodynamic system parameters. In thermodynamic response theory equivalence between ensembles is broken, but time correlation functions sampled in different ensembles are connected through the Maxwell relations of thermodynamics generalized to the frequency domain. Different applications of the theory in the field of supercooled liquids are showed. First the full frequency dependent thermodynamic response matrix is extracted from simulations of a binary Lennard Jones liquid. Secondly some simple stochastic models of supercooled liquids are analysed in the framework of linear thermodynamic response theory. In addition low temperature universality of the specific heat is discussed. Analysis of hydrogen bond dynamics in supercooled SPC/E model water shows that there is a separation between a fast (local) time scale, and a slow (collective) time scale in the supercooled regime. Time temperature scaling of the hydrogen bond correlation function is discussed in terms of a diffusion model.