Summation through stochastic drawing of addends under steered morphing

A stochastic methodology for the numerical estimation of sums over a very large number of addends with huge spread of magnitudes is presented as continuation of our recent work in the field of multidimensional integration. The approach is based on the employment of Jarzynski's equality, borrowed from the physical context of thermodynamics of small systems (mainly macromolecular) subjected to driven transformations while all uncontrolled degrees of freedom freely fluctuate. An abstract interpretation of such an equality enables us to convert the sum into an exponential average over the "computational work" required to morph the addends from an initial set of values (taken all equal for simplicity) up to their actual values while the summation indexes are stochastically sampled by means of Importance Sampling Monte Carlo moves. A series of numerical tests reveals the high efficiency of the method in performing summations otherwise unfeasible.