We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of “linear response function” in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process X(s) but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is,...

Molecular motors are nano- or colloidal machines that keep the living cell in a highly ordered, stationary state far from equilibrium. This self-organized order is sustained by the energy transduction of the motors, which couple exergonic or 'downhill' processes to endergonic or 'uphill' processes. A particularly interesting case is provided by the chemomechanical coupling of cytoskeletal motors which use the chemical energy released during ATP hydrolysis in order to generate mechanical forces and...