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We present a computational strategy for the evaluation of multidimensionalintegrals on hyper-rectangles based on Markovian stochastic exploration of theintegration domain while the integrand is being morphed by starting from aninitial appropriate profile. Thanks to an abstract reformulation of Jarzynski'sequality applied in stochastic thermodynamics to evaluate the free-energyprofiles along selected reaction coordinates via non-equilibriumtransformations, it is possible to cast the original integral into theexponential average of the distribution of the pseudo-work (that we may term"computational work") involved in doing the function morphing, which isstraightforwardly solved. Several tests illustrate the basic implementation ofthe idea, and show its performance in terms of computational time, accuracy andprecision. The formulation for integrand functions with zeros and possible signchanges is also presented. It will be stressed that our usage of Jarzynski'sequality shares similarities with a practice already known in statistics asAnnealed Importance Sampling (AIS), when applied to computation of thenormalizing constants of distributions. In a sense, here we dress the AIS withits "physical" counterpart borrowed from statistical mechanics.

Multidimensional integration through Markovian sampling under steered function morphing: a physical guise from statistical mechanics