Statistical physics and applied geosciences: some results and perspectives

Abstract

Statistical physics and applied geosciences: some results and perspectives Physique statistique et géosciences appliquées : quelques résultats et perspectives

Random fields and up scaling, towards a more predictive probabilistic quantitative hydrogeology

“…Notice that the primary random mathematical objects are functions or fields that are characterized by an infinite number of degrees of freedom. So the most natural embedding formalism that encompasses it is the so called field-theory employed in both statistical mechanics or particle physics [Noetinger, 2020, Hristopulos, 2020. Another related issue that was pointed-out by Tarantola [2005] is that working with continuous variables implies that there is not a reference entropy measure allowing to quantify easily the information of a geostatistical distribution: the overall results are sensitive to the coordinate system used by the modeller.…”

“…That implies that some systematic workflow is to be built in order to reduce the number of dimensions of the effective working space under consideration. As that situation presents some similarities with statistical physics, some bridges between both disciplines can be expected: a description of these connections may be found in Noetinger [2020]. To sumup, similar issues are at the heart of one the most active area of complex systems understanding, the socalled spin glasses for which G Parisi was awarded the 2021 Nobel prize in physics [Mézard et al, 1987, Zdeborová and Krz ąkała, 2007, Zdeborová and Krzakala, 2016.…”