### abstract

- Maximum entropy principle is widely used for the de- termination of equilibrium distribution (see, eg, Ref. 1, for the relativistic case see Ref. 2). The well-known canon- ical distributions are obtained with an assumption of a free energy exchange among the degrees of freedom. This as- sumption is fulfilled when collisions are sufficiently fre- quent. It does not hold in a collisionless plasma within a strong magnetic field. A particle energy in a magnetic field ej is determined by the momentum pI along the magnetic field and the angular momentum projection j onto the mag- netic field direction … P,' heB 1 eic2m+-& j+y , i=CP,jl- ( 1 (1) … There are three extensive parameters of the system: energy E = B eini, momentum component along the magnetic field P = Z pzini, and the angular momentum projection onto the magnetic field J = Z jini, where ni is the particle num- ber in the state i. Let us choose the reference frame, where P = 0. It is …