  Dissipative processes cause collisionless plasmas in many systems to develop
nonthermal particle distributions with broad power-law tails. The prevalence of
power-law energy distributions in space/astrophysical observations and kinetic
simulations of systems with a variety of acceleration and trapping (or escape)
mechanisms poses a deep mystery. We consider the possibility that such
distributions can be modeled from maximum-entropy principles, when accounting
for generalizations beyond the Boltzmann-Gibbs entropy. Using a dimensional
representation of entropy (related to the Renyi and Tsallis entropies), we
derive generalized maximum-entropy distributions with a power-law tail
determined by the characteristic energy scale at which irreversible dissipation
occurs. By assuming that particles are typically energized by an amount
comparable to the free energy (per particle) before equilibrating, we derive a
formula for the power-law index as a function of plasma parameters for magnetic
dissipation in systems with sufficiently complex topologies. The model
reproduces several results from kinetic simulations of relativistic turbulence
and magnetic reconnection.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics;Plasma Physics;Space Physics