{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:26:10Z","timestamp":1760243170511,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T00:00:00Z","timestamp":1447718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed.<\/jats:p>","DOI":"10.3390\/sym7042134","type":"journal-article","created":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T10:23:41Z","timestamp":1447755821000},"page":"2134-2149","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes"],"prefix":"10.3390","volume":"7","author":[{"given":"David","family":"Jou","sequence":"first","affiliation":[{"name":"Departament de F\u00edsica, Universitat Aut\u00f2noma de Barcelona, Bellaterra 08193, Spain"},{"name":"Institut d\u2019Estudis Catalans, Carme 47, Barcelona 08001, Spain"}]},{"given":"Michele","family":"Sciacca","sequence":"additional","affiliation":[{"name":"Departament de F\u00edsica, Universitat Aut\u00f2noma de Barcelona, Bellaterra 08193, Spain"},{"name":"Dipartimento di Scienze Agrarie e Forestali, Universit\u00e0 di Palermo, Viale delle Scienze, Palermo 90128, Italy"},{"name":"Istituto Nazionale di Alta Matematica, Roma 00185 , Italy"}]},{"given":"Maria","family":"Mongiov\u00ec","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Alta Matematica, Roma 00185 , Italy"},{"name":"Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica (DICGIM), Universit\u00e0 di Palermo, Viale delle Scienze, Palermo 90128, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2015,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Dienes, K., and Lennek, M. (2004). Adventures in thermal duality. I. Extracting closed-form solutions for finite-temperature effective potentials in string theory. Phys. Rev. D, 70.","DOI":"10.1103\/PhysRevD.70.126005"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Dienes, K., and Lennek, M. (2004). Adventures in thermal duality. II. Towards a duality-covariant string thermodynamics. Phys. Rev. D, 70.","DOI":"10.1103\/PhysRevD.70.126006"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hewitt, M. (2015). Thermal duality and gravitational collapse. J. Phys., 631.","DOI":"10.1088\/1742-6596\/631\/1\/012076"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Biswas, T., Cembranos, J.A.R., and Kapusta, J.I. (2010). Thermal duality and Hagedorn transition from p-adic strings. Phys. Rev. Lett., 104.","DOI":"10.1007\/JHEP10(2010)048"},{"key":"ref_5","first-page":"125","article-title":"Studies in thermal and dynamical duality and thermodynamics of microblack holes","volume":"Volume 4","author":"Sciacca","year":"2011","journal-title":"Bollettino di Matematica Pura e Applicata"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chaudhuri, S. (2002). Finite temperature bosonic closed strings: Thermal duality and the Kosterlitz-Thouless transition. Phys. Rev. D, 65.","DOI":"10.1103\/PhysRevD.65.066008"},{"key":"ref_7","unstructured":"Zee, A. (2010). Quantum Field Theory in a Nutshell, Princeton University Press."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zwiebach, B. (2009). A First Course in String Theory, Cambridge University Press.","DOI":"10.1017\/CBO9780511841620"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jou, D., Mongiov\u00ec, M., and Sciacca, M. (2011). Duality relation between radiation thermodynamics and cosmic string loop thermodynamics. Phys. Rev. D, 83.","DOI":"10.1103\/PhysRevD.83.103526"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Jou, D., Mongiov\u00ec, M., and Sciacca, M. (2014). A duality-invariant Einstein\u2014Planck relation and its consequences on micro black holes. Int. J. Mod. Phys. D, 70.","DOI":"10.1142\/S0218271814500187"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Jou, D., Mongiov\u00ec, M., and Sciacca, M. (2015). Thermal duality and thermodynamics of micro black holes. Int. J. Mod. Phys. D, 24.","DOI":"10.1142\/S021827181550087X"},{"key":"ref_12","unstructured":"Vilenkin, A., and Shellard, E.P.S. (2000). Cosmic Strings and Other Topological Defects, Cambridge University Press."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Dubath, F., Polchinski, J., and Rocha, J.V. (2008). Cosmic string loops, large and small. Phys. Rev. D, 77.","DOI":"10.1103\/PhysRevD.77.123528"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Lorenz, L., Ringeval, C., and Sakellariadou, M. (2010). Cosmic string loop distribution on all length scales and at any redshift. J. Cosmol. Astropart. Phys., 2010.","DOI":"10.1088\/1475-7516\/2010\/10\/003"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Battye, R., and Moss, A. (2010). Updated constraints on the cosmic string tension. Phys. Rev. D, 82.","DOI":"10.1103\/PhysRevD.82.023521"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Blanco-Pillado, J.J., Olum, K.D., and Shlaer, B. (2014). Number of cosmic string loops. Phys. Rev. D, 89.","DOI":"10.1103\/PhysRevD.89.023512"},{"key":"ref_17","first-page":"231","article-title":"Dark Energy and Dark Matter: Observations, Experiments and Theories","volume":"Volume 36","author":"Buchert","year":"2009","journal-title":"EAS Publications Series"},{"key":"ref_18","unstructured":"Perivolaropoulos, L. (2007). The Invisible Universe: Dark Matter and Dark Energy, Springer."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1038\/31647","article-title":"Tests of quantum gravity from observations of \u03b3-ray bursts","volume":"393","author":"Ellis","year":"1998","journal-title":"Nature"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Amelino-Camelia, G. (2013). Quantum-spacetime phenomenology. Living Rev. Relativ., 16.","DOI":"10.12942\/lrr-2013-5"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Mattingly, D. (2005). Modern tests of lorentz invariance. Living Rev. Relativ., 8.","DOI":"10.12942\/lrr-2005-5"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1016\/j.astropartphys.2011.01.007","article-title":"Search for lorentz invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944","volume":"34","author":"Abramowski","year":"2011","journal-title":"Astropart. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/j.asr.2010.07.025","article-title":"Lorentz symmetry breaking studies with photons from astrophysical observations","volume":"47","author":"Bolmont","year":"2011","journal-title":"Adv. Sp. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.physletb.2008.08.053","article-title":"Probing quantum gravity using photons from a flare of the active galactic nucleus markarian 501 observed by the magic telescope","volume":"668","author":"Albert","year":"2008","journal-title":"Phys. Lett. B"},{"key":"ref_25","unstructured":"Callen, E.B. (1985). Themodynamics and an Introduction to Thermostatics, Wiley."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jou, D., Mongiov\u00ec, M., and Sciacca, M. (2014). Spectral energy distribution and generalized wien\u2019s law for photons and cosmic string loops. Phys. Scr., 89.","DOI":"10.1088\/0031-8949\/89\/7\/075002"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/s10509-012-1349-2","article-title":"Steady Flow cosmological model","volume":"344","author":"Casado","year":"2013","journal-title":"Astrophys. Sp. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Jou, D., and Mongiov\u00ec, M. (2011). Duality-invariant Einstein-Planck relation and the speed of light at very short wavelengths. Phys. Rev. D, 84.","DOI":"10.1103\/PhysRevD.84.107303"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1142\/S021827181102007X","article-title":"World-crystal uncertainty principle and micro black holes","volume":"20","author":"Jizba","year":"2011","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Jizba, P., Kleinert, H., and Scardigli, F. (2010). Uncertainty relation on a world crystal and its applications to micro black holes. Phys. Rev. D, 81.","DOI":"10.1103\/PhysRevD.81.084030"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2355","DOI":"10.1088\/0264-9381\/19\/9\/302","article-title":"General logarithmic corrections to black-hole entropy","volume":"19","author":"Das","year":"2002","journal-title":"Class. Quant. Grav."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Chatterjee, A., and Majumdar, P. (2004). Universal Canonical Black Hole Entropy. Phys. Rev. Lett., 92.","DOI":"10.1103\/PhysRevLett.92.141301"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5255","DOI":"10.1103\/PhysRevLett.84.5255","article-title":"Logarithmic correction to the bekenstein-hawking entropy","volume":"84","author":"Kaul","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ghosh, A., and Mitra, P. (2004). Log correction to the black hole area law. Phys. Rev. D, 71.","DOI":"10.1103\/PhysRevD.71.027502"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.physletb.2010.06.019","article-title":"The generalized second law in universes with quantum corrected entropy relations","volume":"691","author":"Radicella","year":"2010","journal-title":"Phys. Lett. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1007\/BF00758976","article-title":"The thermodynamics of a system containing identical black holes and black-body radiation","volume":"20","author":"Landsberg","year":"1988","journal-title":"Gen. Relat. Grav."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/BF00769629","article-title":"Stability of thermal equilibrium for a radiating black hole in a box","volume":"16","author":"Israel","year":"1984","journal-title":"Gen. Relat. Gravit."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1119\/1.1590656","article-title":"Thermodynamics of black holes in a finite box","volume":"71","author":"Custodio","year":"2003","journal-title":"Am. J. Phys."},{"key":"ref_39","first-page":"113","article-title":"Duality Invariant Dispersion Relations for Electromagnetic and Gravitational Waves at Planck Scales","volume":"Volume 5","author":"Sciacca","year":"2012","journal-title":"Bollettino di Matematica Pura e Applicata"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/7\/4\/2134\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:52:16Z","timestamp":1760215936000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/7\/4\/2134"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,17]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,12]]}},"alternative-id":["sym7042134"],"URL":"https:\/\/doi.org\/10.3390\/sym7042134","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2015,11,17]]}}}