Heat Capacity and the Violation of Scaling Laws in Gravitational System

2025/07/28 by Kong, Shi-Bei · 1 citation
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2507.20992

Abstract

In this paper, we examine the scaling laws in gravitational system from the perspective of free energy landscape and the scaling hypothesis. It has been found that for some special black holes, their critical exponents (0,1,2,3) are beyond the mean field theory, and more surprisingly violate the scaling laws. We find that the main reason for the violation of the scaling laws is that the heat capacity at constant volume C_V is 0, so the critical exponent α is often treated as 0, which can not be derived from the scaling hypothesis. We also find that there is a symmetry violation for the two coexistence states ω_l and ω_s.

Citations

• Extended thermodynamical topology of black hole
• Misner-Sharp Energy and P-V Criticality in Quasi-Topological Cosmology
• Quantum anomaly triggers the violation of scaling laws in gravitational system
• Generalized Euler Equation from Effective Action: Implications for the Smarr Formula in AdS Black Holes
• Phase Transitions and Critical Phenomena for the FRW Universe in an Effective Scalar-Tensor Theory
• Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
• Black hole chemistry: thermodynamics with Lambda
• Isolated critical point from Lovelock gravity

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• Equation of the Perfect Fluid in the FRW Universe

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