{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:25:49Z","timestamp":1760228749170,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T00:00:00Z","timestamp":1653004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research, Development and Innovation Office","award":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"],"award-info":[{"award-number":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"]}]},{"name":"Ministry of Information and Technology","award":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"],"award-info":[{"award-number":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"]}]},{"name":"Ministry of Information and Technology","award":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"],"award-info":[{"award-number":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"]}]},{"name":"National Research, Development and Innovation","award":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"],"award-info":[{"award-number":["NKFIH 123815","TUDFO\/51757\/2019-ITM","FIEK-16-1-2016-0007","NKFIH 123815"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. The resulting field equation for the potential of this emergent force is nonlinear and admits the logarithmic potential as a singular solution, suggesting its relevance to the dark matter conundrum. Here, a general analysis of the nonlinear field equation is performed. It is found that the emergent force field exhibits an unsharp crossover between the 1\/r and 1\/r2 forces outside the fluid, depending on a spatial scale characteristic of the present theory to be observationally tested in the context of the dark matter conundrum. Then, the action functional is constructed for the potential of the emergent field, and the field energy is shown to be free from an infrared divergence. A comment is also made on the difference of the present theory to MOND (modified Newtonian dynamics).<\/jats:p>","DOI":"10.3390\/sym14051048","type":"journal-article","created":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T00:18:11Z","timestamp":1653005891000},"page":"1048","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Crossover in Extended Newtonian Gravity Emerging from Thermodynamics"],"prefix":"10.3390","volume":"14","author":[{"given":"Sumiyoshi","family":"Abe","sequence":"first","affiliation":[{"name":"Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China"},{"name":"Institute of Physics, Kazan Federal University, Kazan 420008, Russia"},{"name":"Department of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent, Tashkent 100095, Uzbekistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9396-4073","authenticated-orcid":false,"given":"Peter","family":"V\u00e1n","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Wigner Research Centre for Physics, Konkoly-Thege Mikl\u00f3s \u00fat 29-33, 1121 Budapest, Hungary"},{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, M\u00fcegyetem rkp. 3, 1111 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, Igm\u00e1ndi \u00fat 26, 1112 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/JHEP04(2011)029","article-title":"On the origin of gravity and the laws of Newton","volume":"4","author":"Verlinde","year":"2011","journal-title":"J. High Energy Phys."},{"key":"ref_2","unstructured":"Hossenfelder, S. (2010). Comments on and comments on comments on Verlinde\u2019s paper \u201cOn the origin of gravity and the laws of Newton\u201d. arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16","DOI":"10.21468\/SciPostPhys.2.3.016","article-title":"Emergent gravity and the dark universe","volume":"2","author":"Verlinde","year":"2017","journal-title":"SciPost Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"12018","DOI":"10.1088\/1742-6596\/701\/1\/012018","article-title":"Atoms of spacetime and the nature of gravity","volume":"701","author":"Padmanabhan","year":"2016","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"A1505","DOI":"10.1103\/PhysRev.135.A1505","article-title":"Theory of thermal transport coefficients","volume":"135","author":"Luttinger","year":"1964","journal-title":"Phys. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1103\/PhysRevLett.75.1260","article-title":"Thermodynamics of spacetime: The Einstein equation of state","volume":"75","author":"Jacobson","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"121301","DOI":"10.1103\/PhysRevLett.96.121301","article-title":"Nonequilibrium thermodynamics of spacetime","volume":"96","author":"Eling","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"126505","DOI":"10.1016\/j.physa.2021.126505","article-title":"Emergence of extended Newtonian gravity from thermodynamics","volume":"588","author":"Abe","year":"2022","journal-title":"Physica A"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Binney, J., and Tremaine, S. (2008). Galactic Dynamics, Princeton University Press. [2nd ed.].","DOI":"10.1515\/9781400828722"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1103\/PhysRevD.14.870","article-title":"Notes on black-hole evaporation","volume":"14","author":"Unruh","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6377","DOI":"10.1063\/1.531249","article-title":"The world as a hologram","volume":"36","author":"Susskind","year":"1995","journal-title":"J. Math. Phys."},{"key":"ref_12","unstructured":"De Groot, S.R., and Mazur, P. (1984). Non-Equilibrium Thermodynamics, Dover."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1086\/161130","article-title":"A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis","volume":"270","author":"Milgrom","year":"1983","journal-title":"Astrophys. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10","DOI":"10.12942\/lrr-2012-10","article-title":"Modified Newtonian dynamics (MOND): Observational phenomenology and relativistic extensions","volume":"15","author":"Famaey","year":"2012","journal-title":"Living Rev. Relativ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1139\/cjp-2014-0211","article-title":"MOND theory","volume":"93","author":"Milgrom","year":"2015","journal-title":"Can. J. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"L107","DOI":"10.1086\/182804","article-title":"Extended rotation curves of high-luminosity spiral galaxies. IV. Systematic dynamical properties, Sa\u2192Sc","volume":"225","author":"Rubin","year":"1978","journal-title":"Astrophys. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"A3","DOI":"10.1051\/0004-6361\/201732547","article-title":"Fitting the radial acceleration relation to individual SPARC galaxies","volume":"615","author":"Li","year":"2018","journal-title":"Astron. Astrophys."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sipols, A., and Pavlovich, A. (2020). Dark matter dogma: A study of 214 galaxies. Galaxies, 8.","DOI":"10.3390\/galaxies8020036"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"L12","DOI":"10.3847\/2041-8213\/ac0335","article-title":"A tip of the red giant branch distance of 22.1 \u00b1 1.2 Mpc to the dark matter deficient galaxy NGC 1052\u2013DF2 from 40 orbits of Hubble Space Telescope imaging","volume":"914","author":"Shen","year":"2021","journal-title":"Astrophys. J. Lett."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1048\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:15:08Z","timestamp":1760138108000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,20]]},"references-count":19,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14051048"],"URL":"https:\/\/doi.org\/10.3390\/sym14051048","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,5,20]]}}}