@article{10613, abstract = {Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields.}, author = {Chen, Joe P. and Sau, Federico}, issn = {1024-2953}, journal = {Markov Processes And Related Fields}, keywords = {interacting particle systems, higher-order fields, hydrodynamic limit, equilibrium fluctuations, duality}, number = {3}, pages = {339--380}, publisher = {Polymat Publishing}, title = {{Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems}}, volume = {27}, year = {2021}, }