Eur. Phys. J. B 54, 405-414 (2006)
https://doi.org/10.1140/epjb/e2007-00013-y

Quantum Brownian motion and the second law of thermodynamics

¹ Department of Physics, North Carolina Central University, Durham, NC, 27707, USA
² Institute of Theoretical Physics I, University of Stuttgart, Pfaffenwaldring 57/IV, 70550 Stuttgart, Germany

Corresponding author: ^a hannibal.ikim@gmail.com

Received: 20 October 2006
Published online: 13 January 2007

Abstract

We consider a single harmonic oscillator coupled to a bath at zero temperature. As is well-known, the oscillator then has a higher average energy than that given by its ground state. Here we show analytically that for a damping model with arbitrarily discrete distribution of bath modes and damping models with continuous distributions of bath modes with cut-off frequencies, this excess energy is less than the work needed to couple the system to the bath, therefore, the quantum second law is not violated. On the other hand, the second law may be violated for bath modes without cut-off frequencies, which are, however, physically unrealistic models.