{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T09:24:21Z","timestamp":1648891461001},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:p> We formulate a variational principle of Fermat type for chemical kinetics in heterogeneous reacting systems. The principle is consistent with the notion of \u2018intrinsic reaction coordinate\u2019 (IRC), the idea of \u2018chemical resistance\u2019 (CR) and the second law of thermodynamics. The Lagrangian formalism applies a nonlinear functional of entropy production that follows from classical (single-phase) nonequilibrium thermodynamics of chemically reacting systems or its extension for multiphase systems involving interface reactions and transports. For a chemical flux, a \u201claw of bending\u201d is found which implies that \u2014 by minimizing the total resistance \u2014 the chemical ray spanned between two given points takes the shape assuring its relatively large part in a region of lower chemical resistivity (a \u2018rarer\u2019 region of the medium). In effect, the chemical flux bends into the direction that ensures its shape consistent with the longest residence of the chemical complex in regions of lower resistivity. The dynamic programming method quantifies the \u201cchemical rays\u201d and related wavefronts along the reaction coordinate. <\/jats:p>","DOI":"10.1023\/a:1019708629128","type":"journal-article","created":{"date-parts":[[2003,3,15]],"date-time":"2003-03-15T08:06:01Z","timestamp":1047715561000},"page":"257-272","source":"Crossref","is-referenced-by-count":6,"title":["A Fermat-like Principle for Chemical Reactions in Heterogeneous Systems"],"prefix":"10.1142","volume":"09","author":[{"given":"Stanis\u0142aw","family":"Sieniutycz","sequence":"first","affiliation":[{"name":"Faculty of Chemical Engineering, Warsaw University of Technology, 1 Wary\u0144skiego Street, 00\u2013645 Warsaw, Poland"}]}],"member":"219","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"rf1","volume-title":"The Theory of Rate Processes","author":"Glasstone S.","year":"1941"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00572927"},{"key":"rf3","first-page":"2756","volume":"51","author":"Tachibana A.","journal-title":"Theor. Chim. Acta (Berl.)"},{"key":"rf4","first-page":"621","volume":"15","author":"Fukui K.","journal-title":"Int. J. Quant. Chem.: Quantum Chemistry Symposjum"},{"key":"rf5","first-page":"633","volume":"15","author":"Fukui K.","journal-title":"Int. J. Quant. Chem.: Quantum Chemistry Symposjum"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(83)90119-X"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1063\/1.453341"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2509(87)87020-3"},{"key":"rf9","unstructured":"J. S.\u00a0Shiner, Advance in Thermodynamics. Series: Flow, Diffusion and Rate Processes, A Lagrangian formulation of chemical reaction dynamics far from equilibrium\u00a06, eds. S.\u00a0Sieniutycz and P.\u00a0Salamon (Taylor and Francis, New York, 1992)\u00a0pp. 248\u2013282."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02228843"},{"key":"rf12","doi-asserted-by":"crossref","DOI":"10.1149\/1.2426448","volume-title":"Introduction to the Principles of Heterogeneous Catalysis","author":"Thomas J. M.","year":"1967"},{"key":"rf13","volume-title":"Kinetic Models of Catalytic Reactions","author":"Yablonskii G. S.","year":"1983"},{"key":"rf14","volume-title":"Heterogeneous Catalysis","author":"Ioffe I. I.","year":"1985"},{"key":"rf15","volume-title":"Heterogeneous Catalysis","author":"Boreskov G. 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M.","year":"1963"},{"key":"rf24","volume-title":"An Introduction to the Calculus of Variations","author":"Fox Ch.","year":"1963"},{"key":"rf25","volume-title":"Discrete Dynamic Programming","author":"Aris R.","year":"1964"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1016\/S0017-9310(00)00032-6"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1023\/A%3A1019708629128","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:37:49Z","timestamp":1565105869000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1023\/A%3A1019708629128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":24,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,4,17]]},"published-print":{"date-parts":[[2002,9]]}},"alternative-id":["10.1023\/A:1019708629128"],"URL":"https:\/\/doi.org\/10.1023\/a:1019708629128","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}