{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:19:28Z","timestamp":1760059168214,"version":"build-2065373602"},"reference-count":67,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T00:00:00Z","timestamp":1748304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia, Portugal","award":["UID\/QUI\/00100\/2019","UIDB\/00100\/2020"],"award-info":[{"award-number":["UID\/QUI\/00100\/2019","UIDB\/00100\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper concerns interactive Monte Carlo simulations for adiabatic ensembles and a genetic algorithm to research and educational contexts. In the Introduction, we discuss some concepts of thermodynamics, statistical mechanics and ensembles relevant to molecular simulations. The second and third sections of the paper comprise two programs in JavaScript regarding (i) argon in the grand-isobaric ensemble focusing on the direct calculation of entropy, vapor\u2013liquid equilibria and radial distribution functions and (ii) an ideal system of quantized harmonic oscillators in the microcanonical ensemble for the determination of the entropy and Boltzmann distribution, also including the definition of Boltzmann and Gibbs entropies relative to classical systems. The fourth section is concerned with a genetic algorithm program in Java, as a pedagogical alternative to introduce the Second Law of Thermodynamics, which summarizes artificial intelligence methods and the cumulative selection process in biogenesis.<\/jats:p>","DOI":"10.3390\/e27060565","type":"journal-article","created":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T08:12:47Z","timestamp":1748419967000},"page":"565","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Monte Carlo Simulation on Adiabatic Ensembles and a Genetic Algorithm"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2945-6266","authenticated-orcid":false,"given":"Fernando M. 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[2nd ed.].","DOI":"10.1093\/oso\/9780198803195.001.0001"},{"key":"ref_4","unstructured":"Sadus, R.J. (2024). Molecular Simulation of Fluids. Theory, Algorithms, Object-Orientation and Parallel Computing, Elsevier. [2nd ed.]."},{"key":"ref_5","unstructured":"Frenkel, D., and Smit, B. (2023). Understanding Molecular Simulation. From Algorithms to Applications, Elsevier. [3rd ed.]."},{"key":"ref_6","unstructured":"Gould, H., Tobochnik, J., and Christian, W. (2016). An Introduction to Computer Simulation Methods, Addison-Wesley. [3rd ed.]. Available online: https:\/\/www.compadre.org\/osp\/items\/detail.cfm?ID=7375."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1119\/1.4901185","article-title":"Interactive molecular dynamics","volume":"83","author":"Schoeder","year":"2015","journal-title":"Am. J. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hoover, W.G., and Hoover, C.G. (2012). Time Reversibility, Computer Simulation, Algorithms, Chaos, World Scientific. [2nd ed.].","DOI":"10.1142\/8344"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kondepudi, D., and Prigogine, I. (2015). Modern Thermodynamics. From Heat Engines to Dissipative Structures, John Wiley & Sons, Ltd.. [2nd ed.].","DOI":"10.1002\/9781118698723"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9656","DOI":"10.1021\/acs.jpclett.0c03130","article-title":"Advancing Physical Chemistry with Machine Learning","volume":"11","author":"Prezhdo","year":"2020","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cartwright, H. (2008). Using Artificial Intelligence in Chemistry and Biology. A Practical Guide, CRC Press.","DOI":"10.1201\/9780849384141"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Morcos, F. (2021). Information Theory in Molecular Evolution: From Models to Structures and Dynamics. Entropy, 23.","DOI":"10.3390\/e23040482"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3300","DOI":"10.1063\/1.464101","article-title":"Improved propagators for the path integral study of quantum systems","volume":"98","author":"Ramalho","year":"1993","journal-title":"J. Chem. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1063\/1.881258","article-title":"The Physics of J. Willard Gibbs in his Time","volume":"43","author":"Klein","year":"1990","journal-title":"Phys. Today"},{"key":"ref_15","unstructured":"Chandler, D. (1987). Introduction to Modern Statistical Mechanics, Oxford University Press."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"129273","DOI":"10.1016\/j.physa.2023.129273","article-title":"Ergodic observables in non-ergodic systems: The example of the harmonic chain","volume":"630","author":"Baldovin","year":"2023","journal-title":"Phys. A"},{"key":"ref_17","unstructured":"Kelly, J.J. (2025, May 01). Semiclassical Statistical Mechanics. Available online: https:\/\/www.physics.umd.edu\/courses\/Phys603\/kelly\/Notes\/Semiclassical.pdf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"094114","DOI":"10.1063\/5.0021488","article-title":"The central role of entropy in adiabatic ensembles and its application to phase transitions in the grand-isobaric adiabatic ensemble","volume":"153","author":"Desgranges","year":"2020","journal-title":"J. Chem. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3030","DOI":"10.1103\/PhysRevA.32.3030","article-title":"Laplace-transform technique for deriving thermodynamic equations from classical microcanonical ensemble","volume":"32","author":"Pearson","year":"1985","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1080\/00268979300102971","article-title":"Eight physical systems of thermodynamics, statistical mechanics and computer simulations","volume":"80","author":"Graben","year":"1993","journal-title":"Mol. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4100","DOI":"10.1103\/PhysRevA.43.4100","article-title":"Unified treatment of adiabatic ensembles","volume":"43","author":"Graben","year":"1991","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1900014","DOI":"10.1002\/adts.201900014","article-title":"Molecular Dynamics of Open Systems: Construction of a Mean-Field Particle Reservoir","volume":"2","author":"Site","year":"2019","journal-title":"Adv. Theory Simul."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1080\/08927029108022137","article-title":"Grand Molecular Dynamics: A Method for Open Systems","volume":"6","author":"Pettitt","year":"1991","journal-title":"Mol. Simul."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"184107","DOI":"10.1063\/1.4712023","article-title":"Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. I. Thermodynamic properties in the bulk and at the liquid-vapor phase boundary","volume":"136","author":"Desgranges","year":"2012","journal-title":"J. Chem. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"064112","DOI":"10.1103\/PhysRevE.107.064112","article-title":"Classical statistical mechanics in the (\u03bc,V, L) and (\u03bc, p, R) ensembles","volume":"107","author":"Meier","year":"2023","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"8816","DOI":"10.1063\/1.477552","article-title":"Microcanonical Monte Carlo simulation of thermodynamic properties","volume":"109","author":"Lustig","year":"1998","journal-title":"J. Chem. Phys."},{"key":"ref_27","unstructured":"(2025, May 01). Thermodynamics and Statistical Mechanics of Small Systems. Special Issue Edited by Puglisi, A., Sarracino, A., Vulpani, A., Entropy Journal. 2017\u20132018., Available online: https:\/\/www.mdpi.com\/journal\/entropy\/special_issues\/small_systems."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.theochem.2010.01.005","article-title":"Phase Transitions, coexistence and crystal growth dynamics in ionic nanoclusters: Theory and Simulation","volume":"946","author":"Rodrigues","year":"2010","journal-title":"J. Mol. Struct. Theochem"},{"key":"ref_29","unstructured":"Callen, H.B. (1985). Thermodynamics and an Introduction to Thermostatistics, John Wiley & Sons. [2nd ed.]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2263","DOI":"10.1063\/1.464207","article-title":"Monte Carlo simulations at constant chemical potential and pressure","volume":"98","author":"Ray","year":"1993","journal-title":"J. Chem. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"084113","DOI":"10.1063\/5.0083458","article-title":"Entropy determination for mixtures in the adiabatic grand-isobaric ensemble","volume":"156","author":"Desgranges","year":"2022","journal-title":"J. Chem. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cplett.2018.11.009","article-title":"Detrmination of mixture properties via a combined Expanded Wang-Landau simulations\u2014Machine Learning approach","volume":"715","author":"Desgranges","year":"2019","journal-title":"Chem. Phys. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1119\/1.1399044","article-title":"Computer simulation of fluid phase transitions","volume":"69","author":"Wilding","year":"2001","journal-title":"Am. J. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"9915","DOI":"10.1063\/1.1572463","article-title":"Direct calculation of liquid-vapor phase equilibria from transition matrix Monte Carlo simulation","volume":"118","author":"Errington","year":"2003","journal-title":"J. Chem. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1119\/1.4921392","article-title":"Gibbs ensemble Monte Carlo","volume":"83","author":"Fartaria","year":"2015","journal-title":"Am. J. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"169","DOI":"10.12921\/cmst.2015.21.04.001","article-title":"The Lennard-Jones Fluid in the Liquid-Vapour Critical Region","volume":"21","author":"Heyes","year":"2015","journal-title":"Comput. Methods Sci. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1021\/ed051p250","article-title":"A computer problem in statistical thermodynamics","volume":"51","author":"Schettler","year":"1974","journal-title":"J. Chem. Educ."},{"key":"ref_38","unstructured":"Dessaux, O., Goudmand, P., and Langrand, F. (1982). Thermodynamique Statistique Chimique, Dunod Universit\u00e9. [2nd ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1119\/1.18490","article-title":"A different approach to introducing statistical mechanics","volume":"65","author":"Moore","year":"1997","journal-title":"Am. J. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1119\/1.3502501","article-title":"The Statistical Interpretation of Entropy: An Activity","volume":"48","author":"Timberlake","year":"2010","journal-title":"Phys. Teach."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1119\/1.3623416","article-title":"Enhancing the understandin of entropy through computation","volume":"79","author":"Salagaram","year":"2011","journal-title":"Am. J. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1119\/1.17732","article-title":"Entropy and the second Law: A pedagogical alternative","volume":"62","author":"Baierlein","year":"1994","journal-title":"Am. J. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1021\/ed100922x","article-title":"Entropy: Order or Information","volume":"88","year":"2011","journal-title":"J. Chem. Educ."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1063\/1.883034","article-title":"A Fresh Look at Entropy and the Second Law of Thermodynamics","volume":"53","author":"Lieb","year":"2000","journal-title":"Phys. Today"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Wolfram, S. (2025, May 01). Computational Foundations for the Second Law of Thermodynamics. 3 February 2023. Available online: https:\/\/writings.stephenwolfram.com\/2023\/02\/computational-foundations-for-the-second-law-of-thermodynamics\/.","DOI":"10.31855\/df530c30-d54"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0010-4655(95)00075-Q","article-title":"Hypervolumes in microcanonical Monte Carlo","volume":"90","author":"Ramalho","year":"1995","journal-title":"Comput. Phys. Comm."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1119\/1.4895828","article-title":"Gibbs, Boltzmann, and negative temperatures","volume":"83","author":"Frenkel","year":"2015","journal-title":"Am. J. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"072001","DOI":"10.1088\/1361-6633\/aac18c","article-title":"Thermodynamics of finite systems: A key issues review","volume":"81","author":"Swendsen","year":"2018","journal-title":"Rep. Prog. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"125023","DOI":"10.1063\/5.0073086","article-title":"A comparison of Boltzmann and Gibbs definitions of microcanonical entropy of small syatems","volume":"11","author":"Shirts","year":"2021","journal-title":"AIP Adv."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"9263","DOI":"10.1021\/acs.jpclett.4c02400","article-title":"Resolving the Debate between Boltzmann and Gibbs Entropy: Relative Energy Window Eliminates Thermodynamic Inconsistencies and Allows Negative Absolute Temperatures","volume":"15","author":"Rajan","year":"2024","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"4061","DOI":"10.1103\/PhysRevA.44.4061","article-title":"Microcanonical ensemble Monte Carlo method","volume":"44","author":"Ray","year":"1991","journal-title":"Phys. Rev. A"},{"key":"ref_52","unstructured":"(2025, May 01). Infinite Monkey Theorem. Posted by Wikipedia. Available online: https:\/\/en.wikipedia.org\/wiki\/Infinite_monkey_theorem."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"100171","DOI":"10.1016\/j.fraope.2024.100171","article-title":"A numerial evalutaion of the Finite Monkeys Theorem","volume":"9","author":"Woodcock","year":"2024","journal-title":"Frankl. Open"},{"key":"ref_54","unstructured":"Bent, H.A. (1965). The Second Law. An Introduction to Classical and Statistical Thermodynamics, Oxford University Press."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Dawkins, R. (1996). The Blind Watchmaker, W.W. Norton & Company. [2nd ed.].","DOI":"10.1142\/9789812832061_0004"},{"key":"ref_56","unstructured":"Freeman, J.A. (1994). Simulating Neural Networks with Mathematica, Addison Wesley."},{"key":"ref_57","unstructured":"(2025, May 01). Phyton Version of Weasel. Posted by GitHub. Available online: https:\/\/github.com\/explosion\/weasel."},{"key":"ref_58","unstructured":"Cartwright, H.G. (1995). Applications of Artificial Intelligence in Chemistry. Oxford Chemistry Primers, Oxford University Press."},{"key":"ref_59","unstructured":"Zupan, J., and Gasteiger, J. (1999). Neural Networks in Chemistry and Drug Design, Wiley-VCH. [2nd ed.]."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"063307","DOI":"10.1103\/PhysRevE.98.063307","article-title":"Crystal nucleation along an entropic pathway: Teaching liquids how to transition","volume":"98","author":"Desgranges","year":"2018","journal-title":"Phys. Rev E"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.jelechem.2008.07.032","article-title":"Mapping Potential Energy Surfaces by Neural Netwoks: The ethanol\/Au(111) interface","volume":"624","author":"Latino","year":"2008","journal-title":"J. Electroanal. Chem."},{"key":"ref_62","unstructured":"Shwalbe-Koda, D., Hamel, S., Babak, S., and Lordi, V. (2024). Information theory unifies machine learning, uncertainty quantification, and material thermodynamics. arXiv."},{"key":"ref_63","unstructured":"Dembski, W.A., and Ewert, W. (2023). The Design Inference: Eliminating Chance Through Small Probabilities, Discovery Institute Press. [2nd ed.]."},{"key":"ref_64","unstructured":"(2024). The Debate over Creationism vs. Evolution, The Rosen Publishing Group."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1119\/1.2973046","article-title":"Entropy and Evolution","volume":"76","author":"Styer","year":"2008","journal-title":"Am. J. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Kondipudi, D.K., De Bari, B., and Dixon, J.A. (2020). Dissipative Structures, Organisms and Evolution. Entropy, 22.","DOI":"10.3390\/e22111305"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"C\u00e1pek, V., and Sheehan, D.P. (2005). Chalenges of the Second Law of Thermodynamics. Theory and Experiment, Springer.","DOI":"10.1007\/1-4020-3016-9"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/565\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:41:16Z","timestamp":1760031676000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/565"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,27]]},"references-count":67,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["e27060565"],"URL":"https:\/\/doi.org\/10.3390\/e27060565","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,5,27]]}}}