Stochastic Equations in Black Hole Backgrounds and Non-equilibrium Fluctuation Theorems

Abstract

We apply the non-equilibrium fluctuation theorems developed in the statistical physics to the thermodynamics of black hole horizons. In particular, we consider a scalar field in a black hole background. The system of the scalar field behaves stochastically due to the absorption of energy into the black hole and emission of the Hawking radiation from the black hole horizon. We derive the stochastic equations, i.e. Langevin and Fokker-Planck equations for a scalar field in a black hole background in the $\hslash \to 0$ limit with the Hawking temperature $\hslash \kappa /2\pi$ fixed. We consider two cases, one confined in a box with a black hole at the center and the other in contact with a heat bath with temperature different from the Hawking temperature. In the first case, the system eventually becomes equilibrium with the Hawking temperature while in the second case there is an energy flow between the black hole and the heat bath. Applying the fluctuation theorems to these cases, we derive the generalized second law of black hole thermodynamics. In the present paper, we treat the black hole as a constant background geometry. Since the paper is also aimed to connect two different areas of physics, non-equilibrium physics and black holes physics, we include pedagogical reviews on the stochastic approaches to the non-equilibrium fluctuation theorems and some basics of black holes physics.

53 pages

References in corpus (17)

• A nonequilibrium equality for free energy differences
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Steady State Thermodynamics of Langevin Systems
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Relationship between Hawking Radiation and Gravitational Anomalies
• Anomalies, Hawking Radiations and Regularity in Rotating Black Holes
• Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies
• An Action for Black Hole Membranes
• A Quantum Fluctuation Theorem
• Thermal Noise and Stochastic Strings in AdS/CFT
• Brownian motion in AdS/CFT
• Higher-spin Currents and Thermal Flux from Hawking Radiation
• Fluxes of Higher-spin Currents and Hawking Radiations from Charged Black Holes
• Hawking Radiation via Higher-spin Gauge Anomalies
• Holographic Brownian Motion and Time Scales in Strongly Coupled Plasmas
• Higher-spin Gauge and Trace Anomalies in Two-dimensional Backgrounds
• Non-Equilibrium Fluctuations of Black Hole Horizons

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