TY - GEN A1 - Liero, Matthias A1 - Mielke, Alexander A1 - Peletier, Mark A. A1 - Renger, D.R. Michiel T1 - On microscopic origins of generalized gradient structures N2 - Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural origins for these structures. A first microscopic origin of generalized gradient structures is given by the theory of large-deviation principles. While Markovian diffusion processes lead to classical gradient structures, Poissonian jump processes give rise to cosh-type dissipation potentials. A second origin arises via a new form of convergence, that we call EDP-convergence. Even when starting with classical gradient systems, where the dissipation potential is a quadratic functional of the rate, we may obtain a generalized gradient system in the evolutionary -limit. As examples we treat (i) the limit of a diffusion equation having a thin layer of low diffusivity, which leads to a membrane model, and (ii) the limit of difusion over a high barrier, which gives a reaction-diffusion system. KW - Generalized gradient structure KW - gradient system KW - evolutionary Γ-convergence KW - energy-dissipation principle KW - variational evolution KW - relative entropy KW - large-deviation principle Y1 - 2016 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1395 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-13958 ER -