The paper presents a mathematical analysis of the Fluctuation Dissipation Theorem (FDT) in the context of Markov processes. It formalizes the concept of a "linear response function" for Markov processes and shows that for processes out of equilibrium, the response function depends not only on the process itself but also on the perturbation applied to it. The paper characterizes all possible response functions for a given Markov process and demonstrates that at equilibrium, they all satisfy the FDT. The FDT relates the dissipation of dynamics at thermal equilibrium to the macroscopic response to external perturbations. The paper also discusses the FDT in the regime near equilibrium and provides examples of generic Markovian perturbations for different types of processes, including pure jump processes, finite dimensional diffusion processes, and stochastic spin systems. The paper shows that the FDT holds in the limit as time goes to infinity for certain conditions on the initial measure. It also discusses the relationship between the FDT and the Green-Kubo formula, which provides an alternative expression for the dissipation term. The paper concludes with a discussion of the implications of the FDT for non-equilibrium systems and the role of symmetry in the FDT.The paper presents a mathematical analysis of the Fluctuation Dissipation Theorem (FDT) in the context of Markov processes. It formalizes the concept of a "linear response function" for Markov processes and shows that for processes out of equilibrium, the response function depends not only on the process itself but also on the perturbation applied to it. The paper characterizes all possible response functions for a given Markov process and demonstrates that at equilibrium, they all satisfy the FDT. The FDT relates the dissipation of dynamics at thermal equilibrium to the macroscopic response to external perturbations. The paper also discusses the FDT in the regime near equilibrium and provides examples of generic Markovian perturbations for different types of processes, including pure jump processes, finite dimensional diffusion processes, and stochastic spin systems. The paper shows that the FDT holds in the limit as time goes to infinity for certain conditions on the initial measure. It also discusses the relationship between the FDT and the Green-Kubo formula, which provides an alternative expression for the dissipation term. The paper concludes with a discussion of the implications of the FDT for non-equilibrium systems and the role of symmetry in the FDT.