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We treat the problem of adiabatic losses and stochastic particle accelerationin gamma-ray burst (GRB) blast waves that decelerate by sweeping up matter froman external medium. The shocked fluid is assumed to be represented by ahomogeneous expanding shell. The energy lost by nonthermal particles throughadiabatic expansion is converted to the bulk kinetic energy of the outflow,permitting the evolution of the bulk Lorentz factor Gamma of the blast wave tobe self-consistently calculated. The behavior of the system is shown toreproduce the hydrodynamic self-similar solutions in the relativistic andnonrelativistic limits, and the formalism is applicable to scenarios that areintermediate between the adiabatic and fully radiative regimes. Nonthermalparticle energization through stochastic gyroresonant acceleration withmagnetic turbulence in the blast wave is treated by employing energy-gain ratesand diffusive escape timescales based upon expressions derived in thequasilinear regime. If the magnetic field in the shocked fluid approaches itsequipartition value, this process can accelerate escaping particles to>~10^{20} eV energies, consistent with the hypothesis that ultra-high energycosmic rays (UHECRs) are accelerated by GRB blast waves. Due to particletrapping by the magnetic turbulence, only the highest energy particles canescape during the prompt and afterglow phases of a GRB for acceleration by aKolmogorov spectrum of MHD turbulence. Lower energy particles begin to escapeas the blast wave becomes nonrelativistic and shock Fermi acceleration becomesmore important.Comment: 30 pages, 11 figures, ApJ, in press, vol. 555, July 10th, 2001  (introduction rewritten, added references and comparison with previous work

Adiabatic Losses and Stochastic Particle Acceleration in Gamma‐Ray Burst Blast Waves