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 ℏ → 0 limit with the Hawking temperature ℏ κ / 2 π 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.
Highlights
The analogy of the space-time with horizons and thermodynamic systems have been extensively investigated, especially, in the black hole thermodynamics [1]
A black hole behaves like a blackbody with the Hawking temperature TH = κ/2π [2], and energy flowing into the black hole can be identified as the entropy increase of the black hole
An application of the fluctuation theorem to a scalar field in a black hole background is straightforward once we obtain a stochastic equation of motion
Summary
The analogy of the space-time with horizons and thermodynamic systems have been extensively investigated, especially, in the black hole thermodynamics [1]. The second purpose of the paper is to apply the non-equilibrium fluctuation theorem [9]-[10] developed in the statistical physics to the scalar field in the black hole background. An application of the fluctuation theorem to a scalar field in a black hole background is straightforward once we obtain a stochastic equation of motion. The integration leads to an effective stochastic equation for a variable at the stretched horizon This has the same spirit as deriving a Langevin equation of a system in contact with a thermal bath [11, 12, 13]. In the appendix C, we explain the fluctuation theorem for a steady state and derivations of nonlinear generalizations of Green-Kubo formula
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
