Energy extraction from rotating black hole with quintessential energy through the Penrose process

We investigate the geometry, dynamics, and collision mechanisms in the ergoregion of Kerr-Newman-AdS black hole influenced by quintessential energy. Particle splittings within the ergoregion are analyzed, demonstrating their role in energy extraction via the Penrose process. Increased spin elongates the ergosphere, while higher quintessential parameters expand static limits and distort photon regions. Prograde orbits benefit from reduced energy and angular momentum due to frame-dragging, whereas retrograde orbits require higher energy. Quintessential energy weakens the gravitational pull, shifts stable orbit radii, and enhances orbital chaos, as indicated by Lyapunov exponents. The Penrose process demonstrates efficiencies ranging from 5% to 35%, with peak efficiency achieved at high spin, but diminishing with increased charge or quintessential energy due to reduced frame-dragging. We derive the expression for irreducible mass and discuss its dependence on cosmological and quintessence parameters, revealing their role in limiting extractable energy.