Charged oscillator in a heat bath in the presence of a magnetic field & third law of thermodynamics

TL;DR

This paper analytically explores the quantum thermodynamics of a charged oscillator in a magnetic field coupled to a heat bath, demonstrating how different coupling schemes affect the third law of thermodynamics at low temperatures.

Contribution

It introduces a detailed analysis of various coupling schemes and their impact on the third law, highlighting the advantages of velocity-velocities coupling in thermodynamic behavior.

Findings

Finite dissipation changes entropy decay from exponential to power law.

Coordinate-velocities coupling ensures linear vanishing of entropy at T→0.

Velocity-velocities coupling scheme best restores the third law.

Abstract

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.