Routing protocol

Fundamental thermodynamic relation

Physics

Gravitation

Computer network

Mathematical physics

Black hole (networking)

Musical

Black hole thermodynamics

Non-equilibrium thermodynamics

Link-state routing protocol

Entropy (arrow of time)

Phase transition

Phase space

Visual arts

Angular momentum

Holography

Theoretical physics

AdS black hole

Computer science

First law of thermodynamics

Quantum mechanics

Formalism (music)

Routing (electronic design automation)

Rotating black hole

Classical mechanics

Thermodynamics

Classical and Quantum Gravity

A new formalism for thermodynamics of AdS black holes called the restricted phase space thermodynamics (RPST) is proposed. The construction is based on top of Visser’s holographic thermodynamics, but with the AdS radius fixed as a constant. Thus the RPST is free of the ( P , V ) variables but inherits the central charge and chemical potential as a new pair of conjugate thermodynamic variables. In this formalism, the Euler relation and the Gibbs–Duhem equation hold simultaneously with the first law of black hole thermodynamics, which guarantee the appropriate homogeneous behaviors for the black hole mass and the intensive variables. The formalism is checked in detail in the example case of four-dimensional Reissner–Nordström anti-de Sitter black hole in Einstein–Maxwell theory, in which some interesting thermodynamic behaviors are revealed.

Restricted phase space thermodynamics for AdS black holes via holography