Dissipative diamagnetism with anomalous coupling and third law

In this work, low temperature thermodynamic behaviour in the context of dissipative diamagnetism with anomalous coupling is analyzed. We find that finite dissipation substitutes the zero-coupling result of exponential decay of entropy by a power law behaviour at low temperature. For Ohmic bath, entropy vanishes linearly with temperature, $T$, in conformity with Nernst's theorem. It is also shown that entropy decays faster in the presence of anomalous coupling than that of the usual coordinate-coordinate coupling. It is observed that velocity-velocity coupling is the most advantageous coupling scheme to ensure the third law of thermodynamics. It is also revealed that different thermodynamic functions are independent of magnetic field at very low temperature for various coupling schemes discussed in this work.