The quantum thermodynamic functions of a harmonic oscillator coupled to a heat bath through velocity-dependent coupling are obtained analytically. It is shown that both the free energy and the entropy decay fast with the temperature in relation to that of the usual coupling from. This implies that the velocity-dependent coupling helps to ensure the third law of thermodynamics.

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Quantum thermodynamics of open quantum systems: nature of thermal fluctuations

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arXiv:quant-ph/0601096 · Physica E Low-dimensional Systems and Nanostructures

Entropy of a quantum oscillator coupled to a heat bath and implications for quantum thermodynamics

G. W. Ford, Robert F. O’Connell

Published Jul 13, 2005• 31 citations

arXiv HTML PDF

DOI: 10.1016/j.physe.2005.05.004

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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.