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Thermodynamics of the gravity from entropy theory

Ginestra Bianconi*

  • *Contact author: ginestra.bianconi@gmail.com
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Phys. Rev. D 114, 024042 – Published 16 July, 2026

DOI: https://doi.org/10.1103/26kn-thgp

Abstract

The Gravity From Entropy (GfE) action posits that gravity is fundamentally given by the information encoded in the interplay between matter and geometry. The GfE Lagrangian is given by the Geometric Quantum Relative Entropy (GQRE) between the physical metric and the metric induced by matter and curvature, leading to modified gravitational field equations with an emergent dynamical effective dark energy term, which reduce to Einstein’s equations in the low-energy, small-curvature limit. Adopting a thermodynamic viewpoint, we identify the GfE energy density with this emergent effective dark energy term. For homogeneous and isotropic Friedmann-Robertson-Walker spacetimes, we show that GfE universes admit a thermal description: locally, they are characterized by k-temperatures and k-pressures satisfying a first law of GfE thermodynamics. In the low-energy, small-curvature regime with perfect-fluid matter and radiation, GfE solutions are well approximated by Friedmann cosmologies. While the total GQRE per unit volume does not increase, the total entropy of GfE universes is nondecreasing in time. We show that, while the total GQRE per unit volume does not increase, consistent with its nature as a relative entropy, the total entropy of GfE universes is nondecreasing in time. These results provide a thermodynamic interpretation of GfE cosmologies and of general relativity itself, recovered in the low-energy, small-curvature limit of the theory, offering a framework to reconcile local order and complexity with the global increase of entropy in the Universe.

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References (85)

  1. Ginestra Bianconi, Gravity from entropy, Phys. Rev. D 111, 066001 (2025).
  2. Ginestra Bianconi, The quantum relative entropy of the Schwarzschild black hole and the area law, Entropy 27, 266 (2025).
  3. Ginestra Bianconi, Beyond holography: The entropic quantum gravity foundations of anisotropic diffusion, Phys. Rev. E 112, L043301 (2025).
  4. Jacob D. Bekenstein, Black holes and entropy, Phys. Rev. D 7, 2333 (1973).
  5. Jacob D. Bekenstein, Generalized second law of thermodynamics in black-hole physics, Phys. Rev. D 9, 3292 (1974).
  6. Stephen W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).
  7. Edward Witten, Introduction to black hole thermodynamics, Eur. Phys. J. Plus 140, 430 (2025).
  8. David Kubizňák, Robert B. Mann, and Mae Teo, Black hole chemistry: Thermodynamics with lambda, Classical Quantum Gravity 34, 063001 (2017).
  9. Yuki Yokokura, Black hole from entropy maximization, Phys. Rev. D 111, 026023 (2025).
  10. Gary W. Gibbons and Stephen W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738 (1977).
  11. Timothy S. Bunch and Paul C. W. Davies, Quantum field theory in de Sitter space: Renormalization by point-splitting, Proc. R. Soc. A 360, 117 (1978).
  12. Nicholas David Birrell and Paul Charles William Davies, Quantum Fields in Curved Space (Cambirdge University Press, 1984).
  13. Raphael Bousso, Alexander Maloney, and Andrew Strominger, Conformal vacua and entropy in de Sitter space, Phys. Rev. D 65, 104039 (2002).
  14. Raphael Bousso, Adventures in de Sitter space, arXiv:hep-th/0205177.
  15. Robert M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48, R3427 (1993).
  16. Vivek Iyer and Robert M. Wald, Some properties of the Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50, 846 (1994).
  17. Ted Jacobson, Gungwon Kang, and Robert C. Myers, On black hole entropy, Phys. Rev. D 49, 6587 (1994).
  18. Shin-ichi Sasa and Yuki Yokokura, Thermodynamic entropy as a Noether invariant, Phys. Rev. Lett. 116, 140601 (2016).
  19. Ted Jacobson, Thermodynamics of spacetime: The Einstein equation of state, Phys. Rev. Lett. 75, 1260 (1995).
  20. Rong-Gen Cai and Sang Pyo Kim, First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe, J. High Energy Phys. 02 (2005) 050.
  21. Sean M. Carroll and Grant N. Remmen, What is the entropy in entropic gravity?, Phys. Rev. D 93, 124052 (2016).
  22. Ted Jacobson, Entanglement equilibrium and the Einstein equation, Phys. Rev. Lett. 116, 201101 (2016).
  23. Erik Verlinde, On the origin of gravity and the laws of Newton, J. High Energy Phys. 04 (2011) 029.
  24. Curtis Callan and Frank Wilczek, On geometric entropy, Phys. Lett. B 333, 55 (1994).
  25. Goffredo Chirco, Hal M. Haggard, Aldo Riello, and Carlo Rovelli, Spacetime thermodynamics without hidden degrees of freedom, Phys. Rev. D 90, 044044 (2014).
  26. Goffredo Chirco and Stefano Liberati, Nonequilibrium thermodynamics of spacetime: The role of gravitational dissipation, Phys. Rev. D 81, 024016 (2010).
  27. Thanu Padmanabhan, Thermodynamical aspects of gravity: New insights, Rep. Prog. Phys. 73, 046901 (2010).
  28. Philipp Dorau and Albert Much, Quantum relative entropy implies the semiclassical Einstein equations, Phys. Rev. Lett. 136, 091602 (2026).
  29. Gerard’t Hooft, The holographic principle, in Basics and Highlights in Fundamental Physics (World Scientific, Singapore, 2001), pp. 72–100.
  30. Leonard Susskind, The world as a hologram, J. Math. Phys. (N.Y.) 36, 6377 (1995).
  31. Brian Swingle, Entanglement renormalization and holography, Phys. Rev. D 86, 065007 (2012).
  32. Shinsei Ryu and Tadashi Takayanagi, Aspects of holographic entanglement entropy, J. High Energy Phys. 08 (2006) 045.
  33. David D. Blanco, Horacio Casini, Ling-Yan Hung, and Robert C. Myers, Relative entropy and holography, J. High Energy Phys. 08 (2013) 060.
  34. Horacio Casini, Marina Huerta, and Robert C. Myers, Towards a derivation of holographic entanglement entropy, J. High Energy Phys. 05 (2011) 036.
  35. Tatsuma Nishioka, Shinsei Ryu, and Tadashi Takayanagi, Holographic entanglement entropy: An overview, J. Phys. A 42, 504008 (2009).
  36. Thomas Faulkner, Aitor Lewkowycz, and Juan Maldacena, Quantum corrections to holographic entanglement entropy, J. High Energy Phys. 11 (2013) 074.
  37. John D. Barrow, The area of a rough black hole, Phys. Lett. B 808, 135643 (2020).
  38. Giorgio Kaniadakis, Statistical mechanics in the context of special relativity, Phys. Rev. E 66, 056125 (2002).
  39. Constantino Tsallis and Leonardo J. L. Cirto, Black hole thermodynamical entropy, Eur. Phys. J. C 73, 2487 (2013).
  40. Constantino Tsallis and Henrik Jeldtoft Jensen, Extensive composable entropy for the analysis of cosmological data, Phys. Lett. B 861, 139238 (2025).
  41. G. O. Heymans, C. D. Rodríguez-Camargo, G. Scorza, and N. F. Svaiter, The entropy of disorder fields in euclidean Schwarzschild black hole, Ann. Phys. (Amsterdam) 482, 170193 (2025).
  42. Hernando Quevedo, Geometrothermodynamics, J. Math. Phys. (N.Y.) 48, 013506 (2007).
  43. Salvatore Capozziello and Orlando Luongo, Information entropy and dark energy evolution, Int. J. Mod. Phys. D 27, 1850029 (2018).
  44. Salvatore Capozziello, Rocco D’Agostino, and Orlando Luongo, Thermodynamic parametrization of dark energy, Phys. Dark Universe 36, 101045 (2022).
  45. Salvatore Capozziello, Rocco D’Agostino, Alessio Lapponi, and Orlando Luongo, Black hole thermodynamics from logotropic fluids, Eur. Phys. J. C 83, 175 (2023).
  46. Giuseppe Gaetano Luciano, Kaniadakis entropy in extreme gravitational and cosmological environments: A review on the state-of-the-art and future prospects, Eur. Phys. J. B 97, 80 (2024).
  47. Salvatore Capozziello and Mehdi Shokri, Barrow entropies in black hole thermodynamics, Eur. Phys. J. C 85, 200 (2025).
  48. Shin’ichi Nojiri, Sergei D. Odintsov, and Valerio Faraoni, From nonextensive statistics and black hole entropy to the holographic dark universe, Phys. Rev. D 105, 044042 (2022).
  49. Shin’ichi Nojiri, Sergei D. Odintsov, and Tanmoy Paul, Early and late universe holographic cosmology from a new generalized entropy, Phys. Lett. B 831, 137189 (2022).
  50. Daniel Baumann, Cosmology (Cambridge University Press, Cambridge, England, 2022).
  51. Timothy Clifton, George FR Ellis, and Reza Tavakol, A gravitational entropy proposal, Classical Quantum Gravity 30, 125009 (2013).
  52. Joseph Polchinski, String Theory (Cambridge University Press, Cambridge, England, 1998).
  53. Carlo Rovelli and Francesca Vidotto, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory (Cambridge University Press, Cambridge, England, 2015).
  54. Alessandro Codello, Roberto Percacci, and Christoph Rahmede, Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation, Ann. Phys. (Amsterdam) 324, 414 (2009).
  55. Astrid Eichhorn, An asymptotically safe guide to quantum gravity and matter, Front. Astron. Space Sci. 5, 47 (2019).
  56. Jan Ambjørn, Jerzy Jurkiewicz, and Renate Loll, Emergence of a 4D world from causal quantum gravity, Phys. Rev. Lett. 93, 131301 (2004).
  57. Sougato Bose, Anupam Mazumdar, Gavin W. Morley, Hendrik Ulbricht, Marko Toroš, Mauro Paternostro, Andrew A. Geraci, Peter F. Barker, M. S. Kim, and Gerard Milburn, Spin entanglement witness for quantum gravity, Phys. Rev. Lett. 119, 240401 (2017).
  58. Chiara Marletto and Vlatko Vedral, Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity, Phys. Rev. Lett. 119, 240402 (2017).
  59. Sougato Bose, Ivette Fuentes, Andrew A. Geraci, Saba Mehsar Khan, Sofia Qvarfort, Markus Rademacher, Muddassar Rashid, Marko Toroš, Hendrik Ulbricht, and Clara C. Wanjura, Massive quantum systems as interfaces of quantum mechanics and gravity, Rev. Mod. Phys. 97, 015003 (2025).
  60. Huzihiro Araki, Relative entropy of states of von Neumann algebras, Publ. RIMS 11, 809 (1975).
  61. Huzihiro Araki, Mathematical Theory of Quantum Fields (Oxford University Press, USA, 1999).
  62. Masanori Ohya and Dénes Petz, Quantum Entropy and its Use (Springer Science & Business Media, Berlin Heidelberg, 2004).
  63. Jonathan Sorce, Notes on the type classification of von Neumann algebras, arXiv:2302.01958.
  64. Kristan Jensen, Jonathan Sorce, and Antony J. Speranza, Generalized entropy for general subregions in quantum gravity, J. High Energy Phys. 12 (2023) 020.
  65. Edward Witten, APS medal for exceptional achievement in research: Invited article on entanglement properties of quantum field theory, Rev. Mod. Phys. 90, 045003 (2018).
  66. Edmund J. Copeland, Mohammad Sami, and Shinji Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15, 1753 (2006).
  67. Sebastian Bahamonde, Christian G. Böhmer, Sante Carloni, Edmund J. Copeland, Wei Fang, and Nicola Tamanini, Dynamical systems applied to cosmology: Dark energy and modified gravity, Phys. Rep. 775, 1 (2018).
  68. Udaykrishna Thattarampilly and Yunlong Zheng, Inflation from entropy, Eur. Phys. J. C, 85, 1433 (2025).
  69. Udaykrishna Thattarampilly, Yunlong Zheng, and Vishnu Kakkat, Spherically symmetric black holes in gravity from entropy and spontaneous emission, Phys. Rev. D 113, 104002 (2026).
  70. Emanuele Berti, Enrico Barausse, Vitor Cardoso, Leonardo Gualtieri, Paolo Pani, Ulrich Sperhake, Leo C. Stein, Norbert Wex, Kent Yagi, Tessa Baker et al., Testing general relativity with present and future astrophysical observations, Classical Quantum Gravity 32, 243001 (2015).
  71. Enrico Barausse, Emanuele Berti, Thomas Hertog, Scott A. Hughes, Philippe Jetzer, Paolo Pani, Thomas P. Sotiriou, Nicola Tamanini, Helvi Witek, Kent Yagi et al., Prospects for fundamental physics with LISA, Gen. Relativ. Gravit. 52, 1 (2020).
  72. Eleonora Di Valentino, Jackson Levi Said, Adam Riess, Agnieszka Pollo, Vivian Poulin, Adrià Gómez-Valent, Amanda Weltman, Antonella Palmese, Caroline D. Huang, Carsten van de Bruck et al., The cosmoverse white paper: Addressing observational tensions in cosmology with systematics and fundamental physics, Phys. Dark Universe 49, 101965 (2025).
  73. Neil Turok and Latham Boyle, Gravitational entropy and the flatness, homogeneity and isotropy puzzles, Phys. Lett. B 849, 138443 (2024).
  74. Latham Boyle and Neil Turok, Thermodynamic solution of the homogeneity, isotropy and flatness puzzles (and a clue to the cosmological constant), Phys. Lett. B 849, 138442 (2024).
  75. Folkert Kuipers, Quantum theory, gravity and higher order geometry, arXiv:2503.10348.
  76. Vlatko Vedral, The role of relative entropy in quantum information theory, Rev. Mod. Phys. 74, 197 (2002).
  77. Chris J. Isham, Canonical quantum gravity and the problem of time, in Integrable Systems, Quantum Groups, and Quantum Field Theories (Springer, New York, 1993), pp. 157–287.
  78. Carlo Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2004).
  79. Carlo Rovelli and Francesca Vidotto, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory (Cambridge University Press, Cambridge, England, 2015).
  80. Gabriel Herczeg and Andrew Waldron, Contact geometry and quantum mechanics, Phys. Lett. B 781, 312 (2018).
  81. Alessandro Bravetti, Contact geometry and thermodynamics, Int. J. Geom. Methods Mod. Phys. 16, 1940003 (2019).
  82. Alessandro Bravetti, Contact Hamiltonian dynamics: The concept and its use, Entropy 19, 535 (2017).
  83. Richard Arnowitt, Stanley Deser, and Charles W. Misner, Canonical variables for general relativity, Phys. Rev. 117, 1595 (1960).
  84. Rishabh Jha, Introduction to Hamiltonian Formulation of General Relativity and Homogeneous Cosmologies SciPost Physics Lecture Notes (2023), p. 073.
  85. John W. Negele and Henri Orland, Quantum Many-Particle Systems (Westview Press, 1998).

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Phys. Rev. D 114, 024042– Published 16 July, 2026
  • Received 26 October 2025
  • Accepted 11 May 2026
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