Third law of thermodynamics for the dissipative cyclotron motion

We derive the heat capacity and the entropy of an exactly solvable model of a charged particle in the combined presence of a uniform homogeneous magnetic field and a finite dissipative quantum heat bath consisting of non interacting harmonic oscillators. The quantities are calculated from the reduced partition function of the damped system which is calculated using the imaginary time functional integral method within the framework of the well known microscopic system-plus-bath model. Unlike the typical choice of an ohmic spectral density of the bath oscillators, we consider the quantum heat bath is having a spectral density corresponding to a thermal harmonic noise. Subsequently we analyse the specific heat and entropy at low and high temperatures. The specific heat and the entropy obtained satisfy the third law of thermodynamics. The heat capacity vanishes as the temperature approaches its absolute zero value, as predicted by the third law of thermodynamics, and satisfies the classical equipartition theorem at high temperatures.