Irreducibility of Informational Effective Field Theories from Nonlocal Influence Kernels

This work is concerned with the structural classification of effective field theories rather than with the construction of specific phenomenological models.We focus on Informational Effective Field Theories (iEFTs), defined by effective dynamics whose stochastic and dissipative sectors are fixed by calibration against quantum correlators of an underlying theory.The central goal is to determine whether such theories can be reduced, via local field redefinitions or coupling reparametrizations, to conventional closed EFTs with explicit symmetry breaking or ad hoc noise terms.We prove that, whenever the effective dynamics is governed by a genuinely nonlocal influence kernel, such a reduction is impossible.Accordingly, the paper establishes iEFTs as a distinct functional class of effective theories within the broader framework of open and nonequilibrium quantum field theory.