{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T14:36:29Z","timestamp":1790433389049,"version":"4.1.0"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T00:00:00Z","timestamp":1490918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Turbulent flows are known to enhance turbulent transport. It has then even been suggested that turbulence is a state of maximum energy dissipation. In this paper, we re-examine critically this suggestion in light of several recent works around the Maximum Entropy Production principle (MEP) that has been used in several out-of-equilibrium systems. We provide a set of four different optimization principles, based on maximization of energy dissipation, entropy production, Kolmogorov\u2013Sinai entropy and minimization of mixing time, and study the connection between these principles using simple out-of-equilibrium models describing mixing of a scalar quantity. We find that there is a chained-relationship between most probable stationary states of the system, and their ability to obey one of the four principles. This provides an empirical justification of the Maximum Entropy Production principle in this class of systems, including some turbulent flows, for special boundary conditions. Otherwise, we claim that the minimization of the mixing time would be a more appropriate principle. We stress that this principle might actually be limited to flows where symmetry or dynamics impose pure mixing of a quantity (like angular momentum, momentum or temperature). The claim that turbulence is a state of maximum energy dissipation, a quantity intimately related to entropy production, is therefore limited to special situations that nevertheless include classical systems such as shear flows, Rayleigh\u2013B\u00e9nard convection and von K\u00e1rm\u00e1n flows, forced with constant velocity or temperature conditions.<\/jats:p>","DOI":"10.3390\/e19040154","type":"journal-article","created":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T10:35:49Z","timestamp":1490956549000},"page":"154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Is Turbulence a State of Maximum Energy Dissipation?"],"prefix":"10.3390","volume":"19","author":[{"given":"Martin","family":"Mihelich","sequence":"first","affiliation":[{"name":"SPEC, CEA, CNRS, Universit\u00e9 Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5001-5698","authenticated-orcid":false,"given":"Davide","family":"Faranda","sequence":"additional","affiliation":[{"name":"LSCE-IPSL, CEA Saclay l\u2019Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Universit\u00e9 Paris-Saclay, 91191 Gif-sur-Yvette, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Didier","family":"Paillard","sequence":"additional","affiliation":[{"name":"LSCE-IPSL, CEA Saclay l\u2019Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Universit\u00e9 Paris-Saclay, 91191 Gif-sur-Yvette, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"B\u00e9reng\u00e8re","family":"Dubrulle","sequence":"additional","affiliation":[{"name":"SPEC, CEA, CNRS, Universit\u00e9 Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,31]]},"reference":[{"key":"ref_1","first-page":"196","article-title":"The heat transport and spectrum of thermal turbulence","volume":"225","author":"Malkus","year":"1954","journal-title":"Proc. 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