{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T12:24:58Z","timestamp":1778847898636,"version":"3.51.4"},"reference-count":46,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,11]],"date-time":"2017-03-11T00:00:00Z","timestamp":1489190400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It is well known that, in the context of General Relativity, some spacetimes, when described by a congruence of comoving observers, may consist of a distribution of a perfect (non\u2013dissipative) fluid, whereas the same spacetime as seen by a \u201ctilted\u201d (Lorentz\u2013boosted) congruence of observers may exhibit the presence of dissipative processes. As we shall see, the appearance of entropy-producing processes are related to the high dependence of entropy on the specific congruence of observers. This fact is well illustrated by the Gibbs paradox. The appearance of such dissipative processes, as required by the Landauer principle, are necessary in order to erase the different amount of information stored by comoving observers, with respect to tilted ones.<\/jats:p>","DOI":"10.3390\/e19030110","type":"journal-article","created":{"date-parts":[[2017,3,13]],"date-time":"2017-03-13T10:26:18Z","timestamp":1489400778000},"page":"110","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["The Gibbs Paradox, the Landauer Principle and the Irreversibility Associated with Tilted Observers"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0466-128X","authenticated-orcid":false,"given":"Luis","family":"Herrera","sequence":"first","affiliation":[{"name":"Instituto Universitario de F\u00edsica Fundamental y Matem\u00e1ticas, Universidad de Salamanca, Salamanca 37007, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/BF01646266","article-title":"Tilted homogeneous cosmological models","volume":"31","author":"King","year":"1973","journal-title":"Commun. Math. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2666","DOI":"10.1063\/1.524845","article-title":"The equivalence of electromagnetic fields and viscous fluids in general relativity","volume":"22","author":"Tupper","year":"1981","journal-title":"J. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1063\/1.524793","article-title":"Viscous fluid interpretation of electromagnetic fields","volume":"22","author":"Raychaudhuri","year":"1981","journal-title":"J. Math. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1086\/161169","article-title":"Zero-curvature Friedmann-Robertson-Walker models as exact viscous magnetohydrodynamic","volume":"271","author":"Coley","year":"1983","journal-title":"Astrophys. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1007\/BF00759233","article-title":"A new look at FRW cosmologies","volume":"15","author":"Coley","year":"1983","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1007\/BF00778797","article-title":"The equivalence of perfect fluid space-times and viscous magnetohydrodynamic space-times in general relativity","volume":"15","author":"Tupper","year":"1983","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/0375-9601(84)90834-X","article-title":"Exact viscous fluid FRW cosmologies: The case of general k","volume":"100","author":"Coley","year":"1984","journal-title":"Phy. Lett. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2282","DOI":"10.1063\/1.526810","article-title":"On the viscous fluid interpretation of some exact solutions","volume":"26","author":"Carot","year":"1985","journal-title":"J. Math. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1086\/165386","article-title":"Observations and nonstandard FRW models","volume":"318","author":"Coley","year":"1987","journal-title":"Astrophys. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1088\/0264-9381\/9\/1\/012","article-title":"Extended thermodynamics of Friedmann-Robertson-Walker models in the Landau-Lifshitz frame","volume":"9","author":"Calvao","year":"1992","journal-title":"Class. Quantum Gravit."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1007\/BF00759230","article-title":"An exact anisotropic solution of the Einstein-Liouville equations","volume":"15","author":"Ellis","year":"1983","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/BF00760654","article-title":"Exact inhomogeneous Einstein-Liouville solutions in Robertson-Walker space-times","volume":"19","author":"Maharaj","year":"1987","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1023\/A:1018855621348","article-title":"The Expanding Universe","volume":"29","year":"1997","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1023\/A:1018891418565","article-title":"Effect of Inhomogeneity on Cosmological Models","volume":"29","author":"Tolman","year":"1997","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1023\/A:1026726520289","article-title":"Spherically Symmetrical Models in General Relativity","volume":"31","author":"Bondi","year":"1999","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"064036","DOI":"10.1103\/PhysRevD.84.064036","article-title":"Tilted Lemaitre-Tolman-Bondi spacetimes: Hydrodynamic and thermodynamic properties","volume":"84","author":"Herrera","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2941","DOI":"10.1103\/PhysRevD.12.2941","article-title":"Quasispherical gravitational collapse","volume":"12","author":"Szekeres","year":"1975","journal-title":"Phys. Rev. D"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF01608547","article-title":"A class of inhomogeneous cosmological models","volume":"41","author":"Szekeres","year":"1975","journal-title":"Commun. Math. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"044003","DOI":"10.1103\/PhysRevD.86.044003","article-title":"Vorticity and entropy production in tilted Szekeres spacetimes","volume":"86","author":"Herrera","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"083501","DOI":"10.1103\/PhysRevD.88.083501","article-title":"Peculiar Raychaudhuri equation","volume":"88","author":"Tsagas","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/s10509-013-1481-7","article-title":"Bianchi type-V cosmological model with purely magnetic solution","volume":"346","author":"Kumar","year":"2013","journal-title":"Astrophys. Space Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s10509-014-1865-3","article-title":"Dynamics of tilted spherical star and stability of non-tilted congruence","volume":"351","author":"Sharif","year":"2014","journal-title":"Astrophys. Space Sci."},{"key":"ref_23","first-page":"361","article-title":"Tilted Lema\u00eetre model and the dark flow","volume":"60","author":"Fernandez","year":"2014","journal-title":"Proc. Math. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1550014","DOI":"10.1142\/S0218271815500145","article-title":"Structure scalars and super-Poynting vector of tilted Szekeres geometry","volume":"24","author":"Sharif","year":"2015","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"024024","DOI":"10.1103\/PhysRevD.95.024024","article-title":"Role of tilted congruence and f(R) gravity on regular compact objects","volume":"95","author":"Yousaf","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_26","unstructured":"Stephani, H. (1982). Introduction to General Relativity, Cambridge University Press."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1088\/0264-9381\/10\/4\/011","article-title":"Reversibility and spacetime symmetries","volume":"10","author":"Bedran","year":"1993","journal-title":"Class. Quantum Gravit."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1088\/0264-9381\/12\/1\/017","article-title":"On the thermodynamics of tilted and collisionless gases in Friedmann-Robertson-Walker spacetimes","volume":"12","author":"Triginer","year":"1995","journal-title":"Class. Quantum Gravit."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1103\/PhysRev.58.919","article-title":"The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid","volume":"58","author":"Eckart","year":"1940","journal-title":"Phys. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF01326412","article-title":"Zum Paradoxon der Warmeleitungstheorie","volume":"198","year":"1967","journal-title":"Z. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/0003-4916(76)90064-6","article-title":"Nonstationary irreversible thermodynamics: A causal relativistic theory","volume":"100","author":"Israel","year":"1976","journal-title":"Ann. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0375-9601(76)90075-X","article-title":"Thermodynamics of nonstationary and transient effects in a relativistic gas","volume":"58","author":"Israel","year":"1976","journal-title":"Phys. Lett. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/0003-4916(79)90130-1","article-title":"Transient relativistic thermodynamics and kinetic theory","volume":"118","author":"Israel","year":"1979","journal-title":"Ann. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1088\/0034-4885\/51\/8\/002","article-title":"Extended irreversible thermodynamics","volume":"51","author":"Jou","year":"1988","journal-title":"Rep. Prog. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Jou, D., Casas-V\u00e1zquez, J., and Lebon, G. (1993). Extended Irreversible Thermodynamics, Springer.","DOI":"10.1007\/978-3-642-97430-4"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1016\/j.physleta.2012.01.003","article-title":"Reversible dissipative processes, conformal motions and Landau damping","volume":"376","author":"Herrera","year":"2012","journal-title":"Phys. Lett. A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"20150230","DOI":"10.1098\/rsta.2015.0230","article-title":"What is Information?","volume":"374","author":"Adami","year":"2016","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_38","unstructured":"Bais, F.A., and Farmer, J.D. (arXiv, 2007). The Physics of Information, arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1119\/1.1971557","article-title":"Gibbs vs Boltzmann Entropies","volume":"33","author":"Jaynes","year":"1965","journal-title":"Am. J. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","article-title":"Irreversibility and Heat Generation in the Computing Process","volume":"5","author":"Landauer","year":"1961","journal-title":"IBM Res. Dev."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1063\/1.1721463","article-title":"The Negentropy Principle of Information","volume":"24","author":"Brillouin","year":"1953","journal-title":"J. Appl. Phys."},{"key":"ref_42","unstructured":"Brillouin, L. (1964). Scientific Uncertainty and Information, Academic."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Brillouin, L. (1962). Science and Information Theory, Academic.","DOI":"10.1063\/1.3057866"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Kish, L.B., and Granqvist, C.G. (arXiv, 2012). Energy Requirement of Control: Comments on Szilard\u2019s Engine and Maxwell\u2019s Demon, arXiv.","DOI":"10.1209\/0295-5075\/98\/68001"},{"key":"ref_45","first-page":"190","article-title":"Moore\u2019s law and the energy requirement of computing versus performance","volume":"151","author":"Kish","year":"2004","journal-title":"Proc. IEEE"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1088\/0004-637X\/710\/2\/1825","article-title":"A Larger Estimate of the Entropy of the Universe","volume":"710","author":"Egan","year":"2010","journal-title":"Astrophys. J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/110\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:30:13Z","timestamp":1760207413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,11]]},"references-count":46,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["e19030110"],"URL":"https:\/\/doi.org\/10.3390\/e19030110","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,11]]}}}