  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 $\hbar
\rightarrow 0$ limit with the Hawking temperature $\hbar \kappa/2 \pi$ 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.
