Multi-Spin Particle Tunneling and Black Hole Thermodynamics: GUP-Corrected Zitterbewegung and Exponentially Modified Entropy

We investigate how the combined influence of spin-gravity coupling and the Generalized Uncertainty Principle (GUP) modifies the evaporation dynamics of a ( 3 + 1 ) -dimensional Reissner-Nordström (RN) black hole. Using Barut’s covariant zitterbewegung formalism, we derive a spin-dependent, GUP-deformed Hamilton-Jacobi equation governing the tunneling of particles with intrinsic spins s = 1 / 2 , 1 , 3 / 2 , 2 . The resulting corrections to the Hawking temperature reveal that the interplay between spin-curvature coupling and GUP effects introduces distinct thermodynamic behaviors across spin sectors: low-spin particles exhibit enhanced tunneling and dominate early-stage radiation, while higher-spin modes experience progressive suppression, leading to thermodynamic stabilization. Employing an exponentially corrected (EC) entropy model, we compute the modified internal energy, free energy, pressure, and heat capacity, all displaying clear spin-dependent trends. Our analysis reveals a natural hierarchy where fermionic fields drive rapid initial evaporation while bosonic and tensorial modes govern final equilibrium stages, culminating in the emergence of stable Planck-scale remnants with residual mass M res ∝ M P l 2 / ( α 0 m ( s ) ) 1 + 2 / ( 4 s ) 2 . The results demonstrate that spin-gravity interactions and GUP corrections act as natural regulators of black hole evaporation, providing a self-consistent mechanism for remnant formation and offering a potential pathway toward resolving the information loss paradox. This framework represents the first spin-resolved thermodynamic treatment within the Zitterbewegung approach, extending previous GUP-based tunneling analyses to capture the complete thermodynamic evolution across multiple spin sectors.