  We study the thermodynamic properties of a partially ionized hydrogen plasma
in strong magnetic fields, B ~ 10^{12}-10^{13} G, typical of neutron stars. The
properties of the plasma depend significantly on the quantum-mechanical sizes
and binding energies of the atoms, which are strongly modified by thermal
motion across the field. We use new fitting formulas for the atomic binding
energies and sizes, based on accurate numerical calculations and valid for any
state of motion of the atom. In particular, we take into account decentered
atomic states, neglected in previous studies of thermodynamics of magnetized
plasmas. We also employ analytic fits for the thermodynamic functions of
nonideal fully ionized electron-ion Coulomb plasmas. This enables us to
construct an analytic model of the free energy. An ionization equilibrium
equation is derived, taking into account the strong magnetic field effects and
the nonideality effects. This equation is solved by an iteration technique.
Ionization degrees, occupancies, and the equation of state are calculated.
