{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:55:31Z","timestamp":1740149731174,"version":"3.37.3"},"reference-count":52,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T00:00:00Z","timestamp":1540252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["RPG-2014-161"],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"Catalytic surface reaction networks exhibit nonlinear dissipative phenomena, such as bistability. Macroscopic rate law descriptions predict that the reaction system resides on one of the two steady-state branches of the bistable region for an indefinite period of time. However, the smaller the catalytic surface, the greater the influence of coverage fluctuations, given that their amplitude normally scales as the square root of the system size. Thus, one can observe fluctuation-induced transitions between the steady-states. In this work, a model for the bistable catalytic CO oxidation on small surfaces is studied. After a brief introduction of the average stochastic modelling framework and its corresponding deterministic limit, we discuss the non-equilibrium conditions necessary for bistability. The entropy production rate, an important thermodynamic quantity measuring dissipation in a system, is compared across the two approaches. We conclude that, in our catalytic model, the most favorable non-equilibrium steady state is not necessary the state with the maximum or minimum entropy production rate.<\/jats:p>","DOI":"10.3390\/e20110811","type":"journal-article","created":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T06:59:40Z","timestamp":1540364380000},"page":"811","source":"Crossref","is-referenced-by-count":1,"title":["Non-Equilibrium Thermodynamics and Stochastic Dynamics of a Bistable Catalytic Surface Reaction"],"prefix":"10.3390","volume":"20","author":[{"given":"Miguel","family":"Pineda","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering, University College London, Roberts Building, Torrington Place, London WC1E 7JE, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8338-8706","authenticated-orcid":false,"given":"Michail","family":"Stamatakis","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, University College London, Roberts Building, Torrington Place, London WC1E 7JE, UK"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,23]]},"reference":[{"key":"ref_1","unstructured":"Kondepudi, D., and Prigogine, I. (1998). Modern Thermodynamics: From Heat Engines to Dissipative Structures, Wiley."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"104501","DOI":"10.1063\/1.5008858","article-title":"Dissipative structures and irreversibility in nature: Celebrating 100th birth anniversary of Ilya Prigogine (1917\u20132003)","volume":"21","author":"Kondepudi","year":"2017","journal-title":"Chaos"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"14437","DOI":"10.1038\/s41598-017-14485-8","article-title":"Entropy production selects non-equilibrium states in multistable systems","volume":"7","author":"Endres","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1098\/rstb.2009.0295","article-title":"The maximum entropy production principle: Two questions","volume":"365","author":"Martyushev","year":"2010","journal-title":"Phil. Trans. R. Soc. B Rep."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1146\/annurev.pc.31.100180.003051","article-title":"The minimum entropy production principle","volume":"31","author":"Jaynes","year":"1980","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"066403","DOI":"10.1103\/PhysRevE.82.066403","article-title":"Entropy production rate in a flux-driven self-organising system","volume":"82","author":"Kawazura","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1098\/rsif.2008.0476","article-title":"Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schl\u00f6gl model revisited","volume":"6","author":"Vellela","year":"2009","journal-title":"J. R. Soc. Interface"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1002\/qj.642","article-title":"Stability, complexity and the maximum dissipation conjecture","volume":"136","author":"Nicoli","year":"2010","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"L371","DOI":"10.1088\/0305-4470\/38\/21\/L01","article-title":"Maximum entropy production and the fluctuation theorem","volume":"38","author":"Dewar","year":"2005","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9717","DOI":"10.1088\/1751-8113\/40\/31\/N01","article-title":"Comments on a derivation and application of the \u2018Maximum entropy production\u2019 principle","volume":"40","author":"Grinstein","year":"2007","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3501","DOI":"10.1256\/qj.02.212","article-title":"Comment on the connection between stability and entropy production","volume":"129","author":"Nicoli","year":"2003","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Dewar, R.C., Lineweaver, C., Niven, R.K., and Regenauer-Lieb, K. (2014). Beyond the Second Law\u2014 Entropy Poduction and Non-Equilibrium Systems, Springer. Chapter 1.","DOI":"10.1007\/978-3-642-40154-1"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1515\/jnetdy.2010.022","article-title":"Simultaneous extrema in the entropy production for steady-state fluid flow in parallel pipe","volume":"35","author":"Niven","year":"2010","journal-title":"J. Non-Equil. Thermodyn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/BF01469698","article-title":"Stability Criteria and Fluctuations around Nonequilibrium States","volume":"56","author":"Luo","year":"1984","journal-title":"Z. Phys. B Condens. Matter."},{"key":"ref_15","unstructured":"Feynman, R.P., Leighton, R.B., and Sands, M.L. (2006). Feynman Lectures on Physics, Pearson\/Addison-Wesley. Chapter 19."},{"key":"ref_16","first-page":"927","article-title":"The steady state format of global climate","volume":"104","author":"Paltridge","year":"1978","journal-title":"Quart. J. Royal Meteorol. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2005.12.001","article-title":"Maximum entropy production principle in physics, chemistry and biology","volume":"426","author":"Martyushev","year":"2006","journal-title":"Phys. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"L14708","DOI":"10.1029\/2007GL029925","article-title":"Maximum entropy production, cloud feedback, and climate change","volume":"34","author":"Paltridge","year":"2007","journal-title":"Geophys. Res. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/s00114-009-0509-x","article-title":"Non-equilibrium thermodynamics and maximum entropy production in the Earth system: applications and implications","volume":"96","author":"Kleidon","year":"2009","journal-title":"Naturwissenschaften"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3524","DOI":"10.1002\/anie.200800480","article-title":"Reactions at surfaces: From atoms to complexity (Nobel lecture)","volume":"47","author":"Ertl","year":"2008","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1021\/cr00035a012","article-title":"Oscillatory kinetics in heterogeneous catalysis","volume":"95","author":"Imbihl","year":"1995","journal-title":"Chem. Rev."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"11551","DOI":"10.1063\/1.479097","article-title":"Macroscopic and mesoscopic characterization of a bistable reaction system: CO oxidation on Pt(111) surface","volume":"110","author":"Berdau","year":"1999","journal-title":"J. Chem. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"8595","DOI":"10.1063\/1.462312","article-title":"Theoretical modeling of spatiotemporal self-organization in a surface catalyzed reaction exhibiting bistable kinetics","volume":"96","author":"Eiswirth","year":"1992","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"064705","DOI":"10.1063\/1.4928279","article-title":"The role of fluctuations in bistability and oscillations during the H2 + O2 reaction on nanosized rhodium crystals","volume":"143","author":"Grosfils","year":"2015","journal-title":"J. Chem. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.1103\/PhysRevLett.82.1907","article-title":"Fluctuation-Induced Transitions in a Bistable Surface Reaction: Catalytic CO Oxidation on a Pt Field Emitter Tip","volume":"82","author":"Suchorski","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1126\/science.1097513","article-title":"Fluctuations and bistabilities on catalyst nanoparticles","volume":"304","author":"Laurin","year":"2004","journal-title":"Science"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7319","DOI":"10.1063\/1.1507105","article-title":"Fluctuations and bistability in a \u201chybrid\u201d atomistic model for CO oxidation on nanofacets: An effective potential analysis","volume":"117","author":"Liu","year":"2002","journal-title":"J. Chem. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"044701","DOI":"10.1063\/1.2140709","article-title":"Theoretical analysis of internal fluctuations and bistability in CO oxidation on nanoscale surfaces","volume":"124","author":"Pineda","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Chorkendorff, I., and Niemantsverdriet, H. (2003). Concepts of Modern Catalysis and Kinetics, Wiley-VCH.","DOI":"10.1002\/3527602658"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0360-0564(08)60133-9","article-title":"Elementary steps in the catalytic oxidation of carbon monoxide on platinum metals","volume":"28","author":"Engel","year":"1979","journal-title":"Adv. Catal."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2602","DOI":"10.1016\/j.compchemeng.2011.05.008","article-title":"Equivalence of on-lattice stochastic chemical kinetics with the well-mixed chemical master equation in the limit of fast diffusion","volume":"35","author":"Stamatakis","year":"2011","journal-title":"Comput. Chem. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Jansen, A.P.J. (2012). An Introduction to Monte Carlo Simulations of Surface Reactions, Springer.","DOI":"10.1007\/978-3-642-29488-4"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1021\/j100540a008","article-title":"Exact stochastic simulation of coupled chemical reactions","volume":"81","author":"Gillespie","year":"1977","journal-title":"J. Phys. Chem."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"8898","DOI":"10.1063\/1.1688758","article-title":"Fluctuation theorem for nonequilibrium reactions","volume":"120","author":"Gaspard","year":"2004","journal-title":"J. Chem. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6167","DOI":"10.1063\/1.1782391","article-title":"Fluctuation theorem and Onsager reciprocity relations","volume":"121","author":"Andrieux","year":"2004","journal-title":"J. Chem. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7011","DOI":"10.1063\/1.450623","article-title":"Stochastic thermodynamics of nonequilibrium steady states in chemical reaction systems","volume":"12","author":"Mou","year":"1986","journal-title":"J. Phys. Chem."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"126001","DOI":"10.1088\/0034-4885\/75\/12\/126001","article-title":"Stochastic thermodynamics, fluctuation theorems and molecular machines","volume":"75","author":"Seifert","year":"2012","journal-title":"Rep. Prog. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.physa.2014.04.035","article-title":"Ensemble and trajectory thermodynamics: A brief introduction","volume":"418","author":"Esposito","year":"2015","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1103\/RevModPhys.48.571","article-title":"Network theory of microscopic and macroscopic behaviour of master equation systems","volume":"48","author":"Schnakenberg","year":"1976","journal-title":"Rev. Mod. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"224104","DOI":"10.1063\/1.5037045","article-title":"Stochastic thermodynamics and entropy production of chemical reaction systems","volume":"148","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Gardiner, C.W. (1985). Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, Springer. [2nd ed.].","DOI":"10.1007\/978-3-662-02452-2"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.compchemeng.2018.05.003","article-title":"On the stochastic modelling of surface reactions through reflected chemical Langevin equations","volume":"117","author":"Pineda","year":"2018","journal-title":"Comput. Chem. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"104615","DOI":"10.1063\/1.5001303","article-title":"Stochastic approach to irreversible thermodynamics","volume":"27","author":"Nicolis","year":"2017","journal-title":"Chaos"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Wilhelm, T. (2009). The smallest chemical reaction system with bistability. BMC Syst. Biol., 3.","DOI":"10.1186\/1752-0509-3-90"},{"key":"ref_45","unstructured":"Malchow, H., and Schimansky-Geier, L. (1985). Noise and Diffusion in Bistable Non-Equilibrium System, Teubner."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2553","DOI":"10.1103\/PhysRevLett.56.2553","article-title":"Kinetic phase transitions in an irreversible surface-reaction model","volume":"56","author":"Ziff","year":"1986","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"044101","DOI":"10.1063\/1.2428297","article-title":"Stochastic thermodynamics of chemical reaction networks","volume":"126","author":"Schmiedl","year":"2007","journal-title":"J. Chem. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"214112","DOI":"10.1063\/1.3598111","article-title":"Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics","volume":"134","author":"Rao","year":"2011","journal-title":"J. Chem. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.physa.2015.01.073","article-title":"On the stochastic thermodynamics of reactive systems","volume":"428","year":"2015","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"148103","DOI":"10.1103\/PhysRevLett.103.148103","article-title":"Thermodynamic limit of a nonequilibrium steady state: Maxwell-type construction for a bistable biochemical system","volume":"103","author":"Ge","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Vlysidis, M., and Kaznesiss, Y.N. (2018). On differences between deterministic and stochastic models of chemical reactions: Scholg solved with ZI-closure. Entropy, 20.","DOI":"10.3390\/e20090678"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1016\/j.physa.2009.11.024","article-title":"Effects of surface size on minimalistic stochastic models for the catalytic CO oxidation","volume":"389","author":"Pineda","year":"2009","journal-title":"Phys. Stat. Mech. Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/811\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T06:02:14Z","timestamp":1718258534000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/811"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,23]]},"references-count":52,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["e20110811"],"URL":"https:\/\/doi.org\/10.3390\/e20110811","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,10,23]]}}}