{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T10:22:30Z","timestamp":1768472550383,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2010,9,27]],"date-time":"2010-09-27T00:00:00Z","timestamp":1285545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We suggest to consider the spacetime as a non-equilibrium system with a long-term stationary state that possess as a spatio-temporally fluctuating quantity \u00df . These systems can be described by a superposition of several statistics, \u201csuperstatistics\u201d. We propose a Gamma distribution for f(\u00df) that depends on a parameter \u03c11. By means of it the corresponding entropy is calculated, \u03c11 is identified with the probability corresponding to this model. A generalized Newton\u2019s law of gravitation is then obtained following the entropic force formulation. We discuss some of the difficulties to try to get an associated theory of gravity.<\/jats:p>","DOI":"10.3390\/e12092067","type":"journal-article","created":{"date-parts":[[2010,9,27]],"date-time":"2010-09-27T11:23:33Z","timestamp":1285586613000},"page":"2067-2076","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Superstatistics and Gravitation"],"prefix":"10.3390","volume":"12","author":[{"given":"Octavio","family":"Obreg\u00f3n","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Divisi\u00f3n de Ciencias e Ingenier\u00edas, Campus Le\u00f3n, Universidad de Guanajuato, Loma del Bosque No. 103, Fracc. Lomas del Campestre, Le\u00f3n, Guanajuato, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2010,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/S0378-4371(03)00019-0","article-title":"Superstatistics","volume":"322","author":"Beck","year":"2003","journal-title":"Phys. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"051101","DOI":"10.1103\/PhysRevE.78.051101","article-title":"Superstatistical distributions from a maximum entropy principle","volume":"78","author":"Beck","year":"2008","journal-title":"Phys. Rev. E"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Statist. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1016\/S0378-4371(98)00437-3","article-title":"The role of constraints within generalized nonextensive statistics","volume":"261","author":"Tsallis","year":"1998","journal-title":"Physica A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"026106","DOI":"10.1103\/PhysRevE.67.026106","article-title":"Constructing a statistical mechanics for Beck-Cohen superstatistics","volume":"67","author":"Tsallis","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01645742","article-title":"The four laws of black hole mechanics","volume":"31","author":"Bardeen","year":"1973","journal-title":"Commun. Math. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF02345020","article-title":"Particle creation by black holes","volume":"43","author":"Hawking","year":"1975","journal-title":"Commun. Math. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1103\/PhysRevLett.75.1260","article-title":"Thermodynamics of space-time: The Einstein equation of state","volume":"75","author":"Jacobson","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","unstructured":"Verlinde, E.P. (2010). On the origin of gravity and the laws of Newton. arXiv, 1001.0785."},{"key":"ref_10","unstructured":"\u2019t Hooft, G. (1993). Dimensional reduction in quantum gravity. arXiv, gr-qc\/9310026."},{"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","doi-asserted-by":"crossref","first-page":"121301","DOI":"10.1103\/PhysRevLett.96.121301","article-title":"Non-equilibrium thermodynamics of spacetime","volume":"96","author":"Eling","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"024016","DOI":"10.1103\/PhysRevD.81.024016","article-title":"Non-equilibrium thermodynamics of spacetime: The role of gravitational dissipation","volume":"81","author":"Chirco","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_14","unstructured":"Chandrasekhar, S. (1992). The mathematical theory of black holes, Clarendon."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/BF01645515","article-title":"Energy and angular momentum flow into a black hole","volume":"27","author":"Hawking","year":"1972","journal-title":"Commun. Math. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1063\/1.2803795","article-title":"Gravity as an emergent phenomenon: A conceptual description","volume":"939","author":"Padmanabhan","year":"2007","journal-title":"AIP Conf. Proc."},{"key":"ref_17","unstructured":"Gil-Villegas, A., Obreg\u00f3n, O., and Robledo, A. (2010). Unpublished work."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"061501","DOI":"10.1103\/PhysRevD.81.061501","article-title":"Friedmann equations from entropic force","volume":"81","author":"Cai","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"084012","DOI":"10.1103\/PhysRevD.81.084012","article-title":"Notes on entropy force in general spherically symmetric spacetimes","volume":"81","author":"Cai","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ling, Y., and Wu, J.P. (2010). A note on entropic force and brane cosmology. arXiv, 1001.5324.","DOI":"10.1088\/1475-7516\/2010\/08\/017"},{"key":"ref_21","unstructured":"Myung, Y.S. (2010). Entropic force in the presence of black hole. arXiv, 1002.0871."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Banerjee, R., and Majhi, B.R. (2010). Statistical origin of gravity. arXiv, 1003.2312.","DOI":"10.1103\/PhysRevD.81.124006"},{"key":"ref_23","unstructured":"Liu, Y.X., Wang, Y.Q., and Wei, S.W. (2010). Temperature and energy of 4-dimensional black holes from entropic force. arXiv, 1002.1062."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Konoplya, R.A. (2010). Entropic force, holography and thermodynamics for static space-times. arXiv, 1002.2818.","DOI":"10.1140\/epjc\/s10052-010-1424-1"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Cai, Y.F., Liu, J., and Li, H. (2010). Entropic cosmology: A unified model of inflation and late-time acceleration. arXiv, 1003.4526.","DOI":"10.1016\/j.physletb.2010.05.033"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"104011","DOI":"10.1103\/PhysRevD.81.104011","article-title":"Entropic corrections to Friedmann equations","volume":"81","author":"Sheykhi","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_27","unstructured":"Ghosh, S. (2010). Planck scale effect in the entropic force law. arXiv, 1003.0285."},{"key":"ref_28","unstructured":"Smolin, L. (2010). Newtonian gravity in loop quantum gravity. arXiv, 1001.3668."},{"key":"ref_29","unstructured":"Vancea, I.V., and Santos, M.A. (2010). Entropic force law, emergent gravity and the uncertainty principle. arXiv, 1002.2454."},{"key":"ref_30","unstructured":"Zhao, Y. (2010). Entropic force and its fluctuation in Euclidian quantum gravity. arXiv, 1002.4039."},{"key":"ref_31","unstructured":"Munkhammar, J. (2010). Is holographic entropy and gravity the result of quantum mechanics?. arXiv, 1003.1262."},{"key":"ref_32","unstructured":"Modesto, L., and Randono, A. (2010). Entropic corrections to Newton\u2019s law. arXiv, 1003.1998."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1023\/A:1010216126590","article-title":"Entropy using path integrals for quantum black hole models","volume":"33","author":"Sabido","year":"2001","journal-title":"Gen. Rel. Grav."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"084024","DOI":"10.1103\/PhysRevD.74.084024","article-title":"Towards noncommutative quantum black holes","volume":"74","author":"Sabido","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.physletb.2008.09.005","article-title":"Black hole quantum tunnelling and black hole entropy correction","volume":"668","author":"Zhang","year":"2008","journal-title":"Phys. Lett. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.physletb.2008.02.044","article-title":"Quantum tunneling and back reaction","volume":"662","author":"Banerjee","year":"2008","journal-title":"Phys. Lett. B"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/9\/2067\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:03:26Z","timestamp":1760220206000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/9\/2067"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,27]]},"references-count":36,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2010,9]]}},"alternative-id":["e12092067"],"URL":"https:\/\/doi.org\/10.3390\/e12092067","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9,27]]}}}