{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T19:55:11Z","timestamp":1775073311554,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,17]],"date-time":"2024-08-17T00:00:00Z","timestamp":1723852800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["21L03897"],"award-info":[{"award-number":["21L03897"]}]},{"name":"JSPS KAKENHI","award":["24K07358"],"award-info":[{"award-number":["24K07358"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Nucleation is a fundamental and general process at the initial stage of first-order phase transition. Although various models based on the classical nucleation theory (CNT) have been proposed to explain the energetics and kinetics of nucleation, detailed understanding at nanoscale is still required. Here, in view of the homogeneous bubble nucleation, we focus on cavity formation, in which evaluation of the size dependence of free energy change is the key issue. We propose the application of a formula in stochastic thermodynamics, the Jarzynski equality, for data analysis of molecular dynamics (MD) simulation to evaluate the free energy of cavity formation. As a test case, we performed a series of MD simulations with a Lennard-Jones (LJ) fluid system. By applying an external spherical force field to equilibrated LJ liquid, we evaluated the free energy change during cavity growth as the Jarzynski\u2019s ensemble average of required works. A fairly smooth free energy curve was obtained as a function of bubble radius in metastable liquid of mildly negative pressure conditions.<\/jats:p>","DOI":"10.3390\/e26080700","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T07:37:21Z","timestamp":1724053041000},"page":"700","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Free Energy Evaluation of Cavity Formation in Metastable Liquid Based on Stochastic Thermodynamics"],"prefix":"10.3390","volume":"26","author":[{"given":"Issei","family":"Shimizu","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9478-2012","authenticated-orcid":false,"given":"Mitsuhiro","family":"Matsumoto","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brennen, C.E. (1995). Cavitation and Bubble Dyamics, Oxford University Press.","DOI":"10.1093\/oso\/9780195094091.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3688","DOI":"10.1073\/pnas.1014075109","article-title":"Evaporation-induced cavitation in nanofluidic channels","volume":"109","author":"Duana","year":"2012","journal-title":"Porc. Natl. Acad. Sci. USA"},{"key":"ref_3","unstructured":"Thome, J.R. (1990). Enhanced Boiling Heat Transfer, CRC Press. [1st ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1016\/j.applthermaleng.2016.08.063","article-title":"Flow boiling in microchannels: Fundamentals and applications","volume":"115","author":"Karayiannis","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_5","unstructured":"Skripov, V.P. (1974). Metastable Liquids, Wiley."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Debenedetti, P.G. (1997). Metastable Liquids: Concepts and Principles, Princeton University Press. [1st ed.].","DOI":"10.1515\/9780691213941"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7602","DOI":"10.1021\/la9002725","article-title":"Stability Limit of Liquid Water in Metastable Equilibrium with Subsaturated Vapors","volume":"25","author":"Wheeler","year":"2009","journal-title":"Langmuir"},{"key":"ref_8","first-page":"51","article-title":"The Stability Limit and Other Open Questions on Water","volume":"152","author":"Caupin","year":"2013","journal-title":"Adv. Chem. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1007\/BF02811776","article-title":"Bubble Nucleation","volume":"1","author":"Hirth","year":"1970","journal-title":"Metall. Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7627","DOI":"10.1088\/0953-8984\/4\/38\/001","article-title":"Homogeneous nucleation: Theory and experiment","volume":"4","author":"Oxtoby","year":"1992","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1063\/1.4818789","article-title":"Attainable superheating of liquefied gases and their solutions","volume":"39","author":"Baidakov","year":"2013","journal-title":"Low Temp. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4472","DOI":"10.1063\/1.460603","article-title":"Gas-liquid nucleation in Lennard-Jones fluids","volume":"94","author":"Zeng","year":"1991","journal-title":"J. Chem. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1063\/1.1525797","article-title":"Homogeneous bubble nucleation in liquids: The classical theory revisited","volume":"118","author":"Delale","year":"2003","journal-title":"J. Chem. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"244501","DOI":"10.1063\/1.3043570","article-title":"Density functional theory of inhomogeneous liquids. III. Liquid-vapor nucleation","volume":"129","author":"Lutsko","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1140\/epje\/i2014-14111-5","article-title":"Scaled nucleation theory for bubble nucleation of lower alkanes","volume":"37","year":"2014","journal-title":"Eur. Phys. J. E"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0378-3812(97)00278-1","article-title":"Cavitation Processes and Negative Pressure","volume":"144","author":"Kinjo","year":"1998","journal-title":"Fluid Phase Equilibria"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/10893950050148124","article-title":"Cavitation and Bubble Nucleation using Molecular Dynamics Simulation","volume":"4","author":"Park","year":"2000","journal-title":"Microscale Thermophys. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1016\/j.fluiddyn.2008.02.002","article-title":"A study on the growth of cavitation bubble nuclei using large-scale molecular dynamics simulations","volume":"40","author":"Tsuda","year":"2008","journal-title":"Fluid Dyn. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"138030","DOI":"10.1016\/j.cplett.2020.138030","article-title":"Molecular dynamics simulation of cavitation in a Lennard-Jones liquid at negative pressures","volume":"760","author":"Baidakov","year":"2020","journal-title":"Chem. Phys. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"114701","DOI":"10.1088\/1674-1056\/ac588a","article-title":"A study of cavitation nucleation in pure water using molecular dynamics simulation","volume":"31","author":"Xie","year":"2022","journal-title":"Chin. Phys. B"},{"key":"ref_21","unstructured":"Peliti, L., and Pigolotti, S. (2021). Stochastic Thermodynamics: An Introduction, Princeton University Press."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1103\/PhysRevLett.78.2690","article-title":"Nonequilibrium equality for free energy differences","volume":"78","author":"Jarzynski","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"134505","DOI":"10.1063\/1.3486086","article-title":"Molecular simulation study of cavity-generated instabilities in the superheated Lennard-Jones liquid","volume":"133","author":"Torabi","year":"2010","journal-title":"J. Chem. Phys."},{"key":"ref_24","unstructured":"LAMMPS (2024, May 01). Molecular Dynamics Simulator. Available online: https:\/\/www.lammps.org."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"108171","DOI":"10.1016\/j.cpc.2021.108171","article-title":"LAMMPS\u2014A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales","volume":"271","author":"Thompsona","year":"2022","journal-title":"Comput. Phys. Commun."},{"key":"ref_26","unstructured":"OVITO (2024, May 01). Open Visualization Tool. Available online: https:\/\/www.ovito.org\/."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Allen, M.P., and Tildesley, D.J. (2017). Computer Simulation of Liquids, Oxford University Press. [2nd ed.].","DOI":"10.1093\/oso\/9780198803195.001.0001"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1080\/00268978400101201","article-title":"A molecular dynamics method for simulations in the canonical ensemble","volume":"52","year":"1984","journal-title":"Mol. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4177","DOI":"10.1063\/1.467468","article-title":"Constant pressure molecular dynamics algorithms","volume":"101","author":"Martyna","year":"1994","journal-title":"J. Chem. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"036105","DOI":"10.1103\/PhysRevE.69.036105","article-title":"Work of cavity formation inside a fluid using free-energy perturbation theory","volume":"69","author":"Punnathanam","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4248","DOI":"10.1021\/acs.jcim.9b00620","article-title":"Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment","volume":"59","author":"Stephan","year":"2019","journal-title":"J. Chem. Inf. Model."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"112772","DOI":"10.1016\/j.fluid.2020.112772","article-title":"Review and comparison of equations of state for the Lennard-Jones fluid","volume":"523","author":"Stephan","year":"2020","journal-title":"Fluid Phase Equilibria"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1016\/j.applthermaleng.2009.12.017","article-title":"A Molecular Dynamics Simulation of Bubble Nucleation in Homogeneous Liquid under Heating with Constant Mean Negative Presure","volume":"30","author":"Zou","year":"2010","journal-title":"Appl. Therm. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1088\/0022-3727\/18\/4\/009","article-title":"Tensile strength of simple liquids predicted by a model of molecular interactions","volume":"18","author":"Kwak","year":"1985","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/j.fluiddyn.2007.12.006","article-title":"Nano bubble\u2013Size dependence of surface tension and inside pressure","volume":"40","author":"Matsumoto","year":"2008","journal-title":"Fluid Dyn. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"154702","DOI":"10.1063\/1.3493464","article-title":"Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study","volume":"133","author":"Block","year":"2010","journal-title":"J. Chem. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"129565","DOI":"10.1016\/j.colsurfa.2022.129565","article-title":"Molecular dynamics simulation of bulk nanobubbles","volume":"650","author":"Hewage","year":"2020","journal-title":"Colloids Surf. A Physicochem. Eng. Asp."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"e2300499120","DOI":"10.1073\/pnas.2300499120","article-title":"Surface tension of cavitation bubbles","volume":"120","author":"Bosserta","year":"2023","journal-title":"Porc. Natl. Acad. Sci. USA"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1017\/S0370164600041729","article-title":"On the equilibrium of vapour at a curved surface of liquid","volume":"7","author":"Thomson","year":"1872","journal-title":"Proc. R. Soc. Edinb."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1146\/annurev-conmatphys-062910-140506","article-title":"Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale","volume":"2","author":"Jarzynski","year":"2011","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_41","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_42","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"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/8\/700\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:38:16Z","timestamp":1760110696000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/8\/700"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,17]]},"references-count":42,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["e26080700"],"URL":"https:\/\/doi.org\/10.3390\/e26080700","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,17]]}}}