  We construct the grand partition function of the system of chiral fermions in
a uniform magnetic field from Landau levels, through which all thermodynamic
quantities can be obtained. Taking use of Abel-Plana formula, these
thermodynamic quantities can be expanded as series with respect to a
dimensionless variable $b=2eB/T^{2}$. We find that the series expansions of
energy density, pressure, magnetization intensity and magnetic susceptibility
contain a singular term with $\ln b^{2}$, while particle number density,
entropy density and heat capacity are power series of $b^{2}$. The asymptotic
behaviors of these thermodynamic quantities in extreme conditions are also
discussed.
