  The quantum thermodynamic behaviour of a charged oscillator in the presence
of a magnetic field and coupled to a heat bath through different coupling
schemes is obtained analytically. It is shown that finite dissipation
substitutes the zero-coupling result of exponential decay of entropy by a power
law behaviour at low temperature. For the coordinate-coordinates coupling
scheme the low temperature explicit results for the case of Ohmic,
exponentially correlated and more generalized heat bath models are derived. In
all the above mentioned cases free energy and entropy vanish linearly with
temperature ($T$) as $T\to 0$ in conformity with Nernst's theorem. It is seen
that coordinate (velocity)-velocities (coordinates) coupling is much more
beneficial than the coordinate-coordinates coupling to ensure third law of
thermodynamics. The case of radiation heat bath shows $T^3$ decay behaviour for
entropy as $T\to 0$. It is observed that at low temperature free energy and
entropy decay faster for the velocity-velocities scheme than any other coupling
schemes. This implies velocity-velocities coupling scheme is the most
advantageous coupling scheme in restoring the third law of thermodynamics. It
is shown that the low temperature thermodynamic functions are independent of
magnetic field for all the above mentioned cases except the without dissipation
case.
