This paper explores the non-equilibrium thermodynamics near horizons in the context of holography, particularly focusing on black branes and their dual theories in the AdS/CFT correspondence. The authors derive analytic solutions for small perturbations of black branes, which are interpreted as deviations from thermodynamic equilibrium in the dual theory. They calculate quasinormal modes, which are gauge-invariant quantities that describe classical fluctuations of the gravitational background under specific boundary conditions. These solutions are used to construct a conserved stress tensor near the horizon, which can represent dissipative parts of the stress tensor in the dual theory. The paper also discusses the membrane paradigm, where a conserved quantity is defined on the stretched horizon, and shows that this quantity satisfies familiar dispersion relations. The authors calculate the shear viscosity and sound velocity of the dual field theory using holographic methods, and derive bulk viscosity from the equations of motion at the horizon and dispersion relations. The results highlight the importance of boundary conditions at infinity and the suppression of UV information in the near-horizon region.This paper explores the non-equilibrium thermodynamics near horizons in the context of holography, particularly focusing on black branes and their dual theories in the AdS/CFT correspondence. The authors derive analytic solutions for small perturbations of black branes, which are interpreted as deviations from thermodynamic equilibrium in the dual theory. They calculate quasinormal modes, which are gauge-invariant quantities that describe classical fluctuations of the gravitational background under specific boundary conditions. These solutions are used to construct a conserved stress tensor near the horizon, which can represent dissipative parts of the stress tensor in the dual theory. The paper also discusses the membrane paradigm, where a conserved quantity is defined on the stretched horizon, and shows that this quantity satisfies familiar dispersion relations. The authors calculate the shear viscosity and sound velocity of the dual field theory using holographic methods, and derive bulk viscosity from the equations of motion at the horizon and dispersion relations. The results highlight the importance of boundary conditions at infinity and the suppression of UV information in the near-horizon region.