{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:26:19Z","timestamp":1772252779428,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,1,31]],"date-time":"2018-01-31T00:00:00Z","timestamp":1517356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["FIS2015-67616-P"],"award-info":[{"award-number":["FIS2015-67616-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constraints for these systems remain an open question. This is largely due to the lack of a general theory of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements falling under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Secondly, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics. Finally, we comment and discuss where further research should be focused on.<\/jats:p>","DOI":"10.3390\/e20020098","type":"journal-article","created":{"date-parts":[[2018,1,31]],"date-time":"2018-01-31T05:51:17Z","timestamp":1517377877000},"page":"98","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Nonequilibrium Entropic Bounds for Darwinian Replicators"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4183-3733","authenticated-orcid":false,"given":"Jordi","family":"Pi\u00f1ero","sequence":"first","affiliation":[{"name":"ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Doctor Aiguader 88, 08003 Barcelona, Spain"},{"name":"Institut de Biologia Evolutiva, Psg. Barceloneta 37-49, 08003 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricard","family":"Sol\u00e9","sequence":"additional","affiliation":[{"name":"ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Doctor Aiguader 88, 08003 Barcelona, Spain"},{"name":"Institut de Biologia Evolutiva, Psg. Barceloneta 37-49, 08003 Barcelona, Spain"},{"name":"Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1006\/jtbi.1994.1211","article-title":"Physics, computation, and why biology looks so different","volume":"171","author":"Hopfield","year":"1994","journal-title":"J. Theor. Biol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Maynard-Smith, J., and Szathm\u00e1ry, E. (1999). The Origins of Life, Oxford University Press.","DOI":"10.1093\/oso\/9780198504931.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Dyson, F. (1999). Origins of Life, Cambridge University Press.","DOI":"10.1017\/CBO9780511546303"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kauffman, S.A. (1993). The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press.","DOI":"10.1093\/oso\/9780195079517.001.0001"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hofbauer, J., and Sigmund, K. (1998). Evolutionary Games and Population Dynamics, Cambridge University Press.","DOI":"10.1017\/CBO9781139173179"},{"key":"ref_6","unstructured":"Morowitz, H., and Smith, E. (2016). The Origin and Nature of Life on Earth: The Emergence of the Fourth Geosphere, Cambridge University Press."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kauffman, S.A. (2000). Investigations, Oxford University Press.","DOI":"10.1093\/oso\/9780195121049.001.0001"},{"key":"ref_8","unstructured":"Babloyantz, A. (1986). Molecules, Dynamics and Life: An Introduction to Self-Organization of Matter, John Wiley & Sons."},{"key":"ref_9","unstructured":"Nicolis, G., and Prigogine, I. (1989). Exploring Complexity: An Introduction, W.H.Freeman & Co, Ltd."},{"key":"ref_10","unstructured":"Glansdorff, P., and Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability and Fluctuations, John Wiley & Sons, Ltd."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1023\/A:1006611022472","article-title":"Complexity versus uncertiainty: The question of staying alive","volume":"15","author":"Wagensberg","year":"2000","journal-title":"Biol. Philos."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1103\/PhysRevLett.78.2690","article-title":"Nonequilibrium equality for free energy differences","volume":"78","author":"Jarzynksi","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1023\/A:1023208217925","article-title":"Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems","volume":"90","author":"Crooks","year":"1998","journal-title":"J. Stat. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2721","DOI":"10.1103\/PhysRevE.60.2721","article-title":"Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences","volume":"60","author":"Crooks","year":"1999","journal-title":"Phys. Rev. E"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"011107","DOI":"10.1103\/PhysRevE.78.011107","article-title":"Lower bounds on dissipation upon coarse graining","volume":"78","author":"Parrondo","year":"2008","journal-title":"Phys. Rev. E"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"120604","DOI":"10.1103\/PhysRevLett.109.120604","article-title":"Thermodynamics of prediction","volume":"109","author":"Still","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"121923","DOI":"10.1063\/1.4818538","article-title":"Statistical physics of self-replication","volume":"139","author":"England","year":"2013","journal-title":"J. Chem. Phys."},{"key":"ref_18","first-page":"021036","article-title":"Statistical physics of adaptation","volume":"6","author":"Perunov","year":"2016","journal-title":"Phys. Rev. X"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"022102","DOI":"10.1103\/PhysRevE.94.022102","article-title":"Bayesian second law of thermodynamics","volume":"94","author":"Bartolotta","year":"2016","journal-title":"Phys. Rev. E"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1098\/rstb.2006.1912","article-title":"The origin of replicators and reproducers","volume":"361","year":"2006","journal-title":"Philos. Trans. R. Soc. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1006\/jtbi.1996.0389","article-title":"From replicators to reproducers: The first major transitions leading to life","volume":"187","year":"1997","journal-title":"J. Theor. Biol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"20150438","DOI":"10.1098\/rstb.2015.0438","article-title":"Synthetic transitions: Towards a new synthesis","volume":"371","year":"2016","journal-title":"Philos. Trans. R. Soc. B"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Eigen, M., and Schuster, P. (1979). The Hypercycle: A Principle of Natural Self-Organization, Springer.","DOI":"10.1007\/978-3-642-67247-7"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0022-5193(89)80177-8","article-title":"Sub-exponential growth and coexistence of non-enzymatically replicating templates","volume":"138","author":"Gladkih","year":"1989","journal-title":"J. Theor. Biol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1006\/jtbi.2001.2360","article-title":"Survival of replicators with parabolic growth tendency and exponential decay","volume":"212","author":"Scheuring","year":"2001","journal-title":"J. Theor. Biol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s12052-012-0440-z","article-title":"Origins for everyone","volume":"5","author":"Ellington","year":"2012","journal-title":"Evol. Educ. Outreach"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","article-title":"Irreversibility and heat generation in the computing process","volume":"5","author":"Landauer","year":"1961","journal-title":"IBM J. Res. Dev."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1007\/BF02084158","article-title":"The thermodynamics of computation\u2014A review","volume":"21","author":"Bennett","year":"1982","journal-title":"Int. J. Theor. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nphys3230","article-title":"Thermodynamics of information","volume":"11","author":"Parrondo","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1063\/1.1740409","article-title":"High-temperature equation of state by a perturbation method. I. Nonpolar gases","volume":"22","author":"Zwanzig","year":"1954","journal-title":"J. Chem. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/0169-5347(91)90228-P","article-title":"Simple growth laws and selection consequences","volume":"6","year":"1991","journal-title":"Trends Ecol. Evol."},{"key":"ref_32","unstructured":"Maynard-Smith, J., and Szathm\u00e1ry, E. (1995). The Major Transitions in Evolution, Oxford University Press."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/BF00623322","article-title":"Self-organization of matter and the evolution of biological macromolecules","volume":"58","author":"Eigen","year":"1971","journal-title":"Naturwissenchaften"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/BF00450633","article-title":"The hypercycle: A principle of natural self-organization. Part A: Emergence of the hypercycle","volume":"64","author":"Eigen","year":"1977","journal-title":"Naturwissenchaften"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/BF00420631","article-title":"The hypercycle: A principle of natural self-organization. Part B: The abstract hypercycle","volume":"65","author":"Eigen","year":"1977","journal-title":"Naturwissenchaften"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF00439699","article-title":"The hypercycle: A principle of natural self-organization. Part C: The realistic hypercycle","volume":"65","author":"Eigen","year":"1977","journal-title":"Naturwissenchaften"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1038\/nature11549","article-title":"Spontaneous network formation among cooperative RNA replicators","volume":"491","author":"Vaidya","year":"2012","journal-title":"Nature"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1038\/382525a0","article-title":"A self-replicating peptide","volume":"382","author":"Lee","year":"1996","journal-title":"Nature"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1002\/anie.198609322","article-title":"A self-replicating, hexadeoxy nucleotide","volume":"25","year":"1986","journal-title":"Angew. Chem. Int. Ed. Engl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1038\/327346a0","article-title":"Autocatalytic synthesis of a tetranucleotide analogue","volume":"327","author":"Zielinski","year":"1977","journal-title":"Nature"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.cbpa.2004.09.005","article-title":"Minimal self-replicating systems","volume":"8","author":"Paul","year":"2004","journal-title":"Curr. Opin. Chem. Biol."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"M\u00e9ndez, V., Campos, D., and Bartumeus, F. (2014). Stochastic Foundations in Movement Ecology: Anomalous Diffusion, Front Propagation and Random Searches, Springer.","DOI":"10.1007\/978-3-642-39010-4"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Redner, S. (2001). A Guide to First-Passage Processes, Cambridge University Press.","DOI":"10.1017\/CBO9780511606014"},{"key":"ref_44","unstructured":"von Neumann, J., and Burks, A.W. (1966). Theory of Self-Reproducing Automata, University of Illinois Press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1038\/scientificamerican0208-48sp","article-title":"Go forth and replicate","volume":"18","author":"Sipper","year":"2008","journal-title":"Sci. Am."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"9516","DOI":"10.1073\/pnas.0802049105","article-title":"Nonequilibrium generation of information in copolymerization processes","volume":"105","author":"Andrieux","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"158103","DOI":"10.1103\/PhysRevLett.118.158103","article-title":"Fundamental costs in the production and destruction of persistent polymer copies","volume":"118","author":"Ouldridge","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2106","DOI":"10.1021\/ar300027q","article-title":"Ocean-atmosphere interactions in the emergence of complexity in simple chemical systems","volume":"45","author":"Griffith","year":"2012","journal-title":"Acc. Chem. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1007\/BF02101147","article-title":"Studies on evolutioanry and selective properties of hypercycles using a Monte Carlo method","volume":"26","author":"Montero","year":"1987","journal-title":"J. Mol. Evol."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/S0022-5193(88)80049-3","article-title":"Influence of the hypercyclic organization on the error threshold: A stochastic approach","volume":"134","author":"Olarrea","year":"1988","journal-title":"J. Theor. Biol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/2\/98\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:53:11Z","timestamp":1760194391000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/2\/98"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,31]]},"references-count":50,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["e20020098"],"URL":"https:\/\/doi.org\/10.3390\/e20020098","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/225011","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,31]]}}}