{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T08:00:01Z","timestamp":1768032001829,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2012,6,13]],"date-time":"2012-06-13T00:00:00Z","timestamp":1339545600000},"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>From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein\u2013Yang\u2013Mills black holes. In this paper, from the perspective of the state-space surface and chemical Weinhold surface of higher dimensional gravity, we provide the criteria for the local and global statistical stability of an ensemble of topological Einstein\u2013Yang\u2013Mills black holes in arbitrary spacetime dimensions D \u2265 5. Finally, as per the formulations of the thermodynamic geometry, we offer a parametric account of the statistical consequences in both the local and global fluctuation regimes of the topological extremal Einstein\u2013Yang\u2013Mills black holes.<\/jats:p>","DOI":"10.3390\/e14061045","type":"journal-article","created":{"date-parts":[[2012,6,14]],"date-time":"2012-06-14T02:32:26Z","timestamp":1339641146000},"page":"1045-1078","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Thermodynamic Geometry and Topological Einstein\u2013Yang\u2013Mills Black Holes"],"prefix":"10.3390","volume":"14","author":[{"given":"Stefano","family":"Bellucci","sequence":"first","affiliation":[{"name":"INFN-Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044 Frascati, Italy"}]},{"given":"Bhupendra Nath","family":"Tiwari","sequence":"additional","affiliation":[{"name":"INFN-Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044 Frascati, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2012,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1103\/RevModPhys.67.605","article-title":"Riemannian geometry in thermodynamic fluctuation theory","volume":"67","author":"Ruppeiner","year":"1995","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"024016","DOI":"10.1103\/PhysRevD.78.024016","article-title":"Thermodynamic curvature and phase transitions in Kerr\u2013Newman black holes","volume":"78","author":"Ruppeiner","year":"2008","journal-title":"Phy. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1608","DOI":"10.1103\/PhysRevA.20.1608","article-title":"Thermodynamics: A Riemannian geometric model","volume":"20","author":"Ruppeiner","year":"1979","journal-title":"Phys. Rev. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1103\/PhysRevLett.50.287","article-title":"Thermodynamic critical fluctuation theory?","volume":"50","author":"Ruppeiner","year":"1983","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1103\/PhysRevA.27.1116","article-title":"New thermodynamic fluctuation theory using path integrals","volume":"27","author":"Ruppeiner","year":"1983","journal-title":"Phys. Rev. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2200","DOI":"10.1103\/PhysRevA.41.2200","article-title":"Thermodynamic curvature of the multicomponent ideal gas","volume":"41","author":"Ruppeiner","year":"1990","journal-title":"Phys. Rev. A"},{"key":"ref_7","unstructured":"Tiwari, B.N. (2011). On Generalized Uncertainty Principle, LAP Academic Publication."},{"key":"ref_8","unstructured":"Tiwari, B.N. (2011). Sur les corrections de la g\u00e9om\u00e9trie thermodynamique des trous noirs, \u00c9ditions Universitaires Europ\u00e9ennes."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1088\/1126-6708\/2006\/11\/015","article-title":"On the thermodynamic geometry of BTZ black holes","volume":"2006","author":"Sarkar","year":"2006","journal-title":"J. High Energ. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1088\/1126-6708\/2008\/10\/076","article-title":"Thermodynamic geometry and extremal black holes in string theory","volume":"2008","author":"Sarkar","year":"2008","journal-title":"J. High Energ. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2096","DOI":"10.3390\/e12102097","article-title":"On the microscopic perspective of black branes thermodynamic geometry","volume":"12","author":"Bellucci","year":"2010","journal-title":"Entropy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/JHEP05(2010)023","article-title":"An exact fluctuating 1\/2-BPS configuration","volume":"2010","author":"Bellucci","year":"2010","journal-title":"J. High Energ. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"084008","DOI":"10.1103\/PhysRevD.82.084008","article-title":"State-space correlations and stabilities","volume":"82","author":"Bellucci","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1007\/JHEP11(2010)030","article-title":"Thermodynamic geometry and Hawking radiation","volume":"2010","author":"Bellucci","year":"2010","journal-title":"J. High Energ. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5403","DOI":"10.1142\/S0217751X11054978","article-title":"Black strings, black rings and state-space manifold","volume":"26","author":"Bellucci","year":"2011","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1007\/JHEP01(2011)118","article-title":"State-space manifold and rotating black holes","volume":"2011","author":"Bellucci","year":"2011","journal-title":"J. High Energ. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1007\/s10714-006-0306-1","article-title":"Flat information geometries in black hole thermodynamics","volume":"38","author":"Aman","year":"2006","journal-title":"Gen. Rel. Grav."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1142\/S0217751X07034064","article-title":"Thermodynamic geometry and critical behavior of black holes","volume":"22","author":"Shen","year":"2007","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1733","DOI":"10.1023\/A:1026058111582","article-title":"Geometry of black hole thermodynamics","volume":"35","author":"Aman","year":"2003","journal-title":"Gen. Rel. Grav."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"024017","DOI":"10.1103\/PhysRevD.73.024017","article-title":"Geometry of higher-dimensional black hole thermodynamics","volume":"73","author":"Aman","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_21","unstructured":"Tiwari, B.N. (2011). Geometric Perspective of Entropy Function: Embeddings, Spectrum and Convexity, LAP Academic Publication."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1063\/1.431689","article-title":"Metric geometry of equilibrium thermodynamics","volume":"63","author":"Weinhold","year":"1975","journal-title":"J. Chem. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2484","DOI":"10.1063\/1.431635","article-title":"Metric geometry of equilibrium thermodynamics. II. Scaling, homogeneity, and generalized Gibbs-Duhem relations","volume":"63","author":"Weinhold","year":"1975","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1142\/S0217751X11051172","article-title":"On the thermodynamic geometry of hot QCD","volume":"26","author":"Bellucci","year":"2011","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1250055","DOI":"10.1142\/S0217732312500551","article-title":"A geometric approach to correlations and quark number susceptibilities","volume":"27","author":"Bellucci","year":"2010","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1142\/S0217751X11053511","article-title":"Thermodynamic stability of Quarkoniumn bound states","volume":"26","author":"Bellucci","year":"2011","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1103\/PhysRevLett.61.141","article-title":"Particlelike solutions of the Einstein\u2013Yang\u2013Mills equations","volume":"61","author":"Bartnik","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2212","DOI":"10.1103\/PhysRevD.12.2212","article-title":"Solutions for gravity coupled to massless gauge fields","volume":"12","author":"Yasskin","year":"1975","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/978-3-540-88460-6_2","article-title":"Physics of black holes","volume":"769","author":"Winstanley","year":"2009","journal-title":"Lect. Notes Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"104012","DOI":"10.1103\/PhysRevD.67.104012","article-title":"Five-dimensional black hole and particle solution with a non-Abelian gauge field","volume":"67","author":"Okuyama","year":"2003","journal-title":"Phys. Rev. D"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.physletb.2007.11.006","article-title":"Einstein\u2013Yang\u2013Mills black hole solution in higher dimensions by the Wu\u2013Yang Ansatz","volume":"659","author":"Mazharimousavi","year":"2008","journal-title":"Phys. Lett. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"02765","DOI":"10.1088\/0264-9381\/20\/13\/323","article-title":"Particle-like solutions to higher-order curvature Einstein\u2013Yang\u2013Mills systems in d dimensions","volume":"20","author":"Brihaye","year":"2003","journal-title":"Classical Quant. Grav."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/S0370-2693(03)00401-5","article-title":"Higher order curvature generalizations of Bartnick\u2013McKinnon and coloured black hole solutions in d=5","volume":"561","author":"Brihaye","year":"2003","journal-title":"Phys. Lett. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"R4272","DOI":"10.1103\/PhysRevD.52.R4272","article-title":"Cosmic colored black holes","volume":"52","author":"Torii","year":"1995","journal-title":"Phys. Rev. D"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7243","DOI":"10.1103\/PhysRevD.54.7243","article-title":"Cosmological analogues of the Bartnik\u2013McKinnon solutions","volume":"54","author":"Volkov","year":"1996","journal-title":"Phys. Rev. D"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"064015","DOI":"10.1103\/PhysRevD.74.064015","article-title":"Non-Abelian solutions in AdS4 and d=11 supergravity","volume":"74","author":"Mann","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1103\/PhysRevLett.84.1853","article-title":"Stable monopole and Dyon solutions in the Einstein\u2013Yang\u2013Mills theory in asymptotically anti-de Sitter space","volume":"84","author":"Bjoraker","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"245014","DOI":"10.1088\/0264-9381\/25\/24\/245014","article-title":"On the existence of soliton and hairy black hole solutions of su(N) Einstein\u2013Yang\u2013Mills theory with a negative cosmological constant","volume":"25","author":"Baxter","year":"2008","journal-title":"Classical Quant. Grav."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"7338","DOI":"10.1103\/PhysRevD.54.7338","article-title":"Stability analysis of new solutions of the EYM system with a cosmological constant","volume":"54","author":"Brodbeck","year":"1996","journal-title":"Phys. Rev. D"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1088\/0264-9381\/16\/6\/325","article-title":"Existence of stable hairy black holes in su(2) Einstein\u2013Yang\u2013Mills theory with a negative cosmological constant","volume":"16","author":"Winstanley","year":"1999","journal-title":"Classical Quant. Grav."},{"key":"ref_41","unstructured":"Mark, H., and Fenbach, S. (1969). Properties of Matter under Unusual Conditions, Interscience."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1142\/S0217732310032809","article-title":"Topological black holes of (n+1)-dimensional Einstein\u2013Yang\u2013Mills gravity","volume":"25","author":"Bostani","year":"2010","journal-title":"Mod. Phys. Letts. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"044023","DOI":"10.1103\/PhysRevD.81.044023","article-title":"Non-Abelian black holes in D=5 maximal gauged supergravity","volume":"81","author":"Cvetic","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Hubeny, V.E., Minwalla, S., and Rangamani, M. (2011). The fluid\/gravity correspondence. arXiv.","DOI":"10.1142\/9789814350525_0014"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Banerjee, N., Bhattacharya, J., Bhattacharyya, S., Jain, S., Minwalla, S., and Sharma, T. (2012). Constraints on fluid dynamics from equilibrium partition functions. arXiv.","DOI":"10.1007\/JHEP09(2012)046"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/6\/1045\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:50:46Z","timestamp":1760219446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/6\/1045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,13]]},"references-count":45,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2012,6]]}},"alternative-id":["e14061045"],"URL":"https:\/\/doi.org\/10.3390\/e14061045","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,13]]}}}