Thermodynamic Properties of Black Holes and Cosmic Systems

Black holes and large‐scale cosmic structures exhibit thermodynamic behaviour that bridges general relativity, quantum theory and statistical mechanics. The foundational principle is that horizons, whether those of black holes or of cosmological apparent boundaries, carry an entropy proportional to their surface area and radiate as thermal objects with a characteristic temperature. This insight, stemming from the Bekenstein–Hawking relation, implies that spacetime itself possesses microscopic degrees of freedom and that gravitational dynamics can be recast in thermodynamic language. In the cosmological context, applying the first and second laws of thermodynamics to the apparent horizon leads to modified Friedmann equations governing the evolution of the universe. Extensions of the area law via non-additive entropies have been proposed to address outstanding puzzles such as the H₀ and σ₈ tensions, dark-energy dynamics and early-universe inflation. Meanwhile, quantum gravitational corrections to horizon geometry—modelled, for example, by fractal or rough surfaces—suggest substantial modifications to the entropy and lifetime of black holes. Taken together, these developments have highlighted deep interconnections between horizon thermodynamics, cosmic evolution and quantum gravity, pointing towards a unified description of gravitation as an emergent, thermodynamic phenomenon.

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Thermodynamic Properties of Black Holes and Cosmic Systems publication trend

The graph below shows the total number of articles in thermodynamic properties of black holes and cosmic systems across all publications each year (not limited to Nature Index journals).

Technical terms

Bekenstein–Hawking entropy: The entropy of a black hole proportional to its horizon area divided by the Planck area.

Tsallis entropy: A non-additive generalisation of standard entropy, characterised by an exponent that quantifies departure from the area law.

Kaniadakis entropy: A one-parameter relativistic extension of Boltzmann–Gibbs entropy, leading to modified thermodynamic relations.

Apparent horizon: A marginally trapped surface in cosmology that delineates the boundary of observable regions and carries thermodynamic properties.

Friedmann equations: The set of equations derived from general relativity that describe the expansion dynamics of a homogeneous and isotropic universe.

Fractal horizon geometry: A model in which the event-horizon surface is endowed with self-similar, scale-invariant structure, altering its effective area.

References

1. Alleviating both H0 and σ8 tensions in Tsallis cosmology. European Physical Journal C (2024).
2. Corrections to Friedmann equations inspired by Kaniadakis entropy. Physics Letters B (2024).
3. The area of a rough black hole. Physics Letters B (2020).