Evaluation of free energy landscapes from manipulation experiments

A fluctuation relation, which is an extended form of the Jarzynski equality, is introduced and discussed. We show how to apply this relation in order to evaluate the free energy landscape of simple systems. These systems are manipulated by varying the external field coupled with a systems’ internal characteristic variable. Two different manipulation protocols are here considered: in the first case the external field is a linear function of time, in the second case it is a periodic function of time. While for simple mean field systems both the linear protocol and the oscillatory protocol provide a reliable estimate of the free energy landscape, for a simple model of homopolymer the oscillatory protocol turns out to be not reliable for this purpose. We then discuss the possibility of application of the method here presented to evaluate the free energy landscape of real systems, and the practical limitations that one can face in the realization of an experimental set-up.