Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-11-22
Physics
Condensed Matter
Statistical Mechanics
Revised version restricted to harmonic potential. Includes violation of the Clausius inequality, negative energy dispersion, n
Scientific paper
The Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath is exactly solvable. It is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a non-trivial role. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low $T$. Various formulations of the second law are found to be invalid at low $T$. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g. those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale $\hbar/k_BT$ is larger than or comparable to other timescale of the system. They show that there is no general consensus between standard thermodynamics and quantum mechanics.
Allahverdyan Armen E.
Nieuwenhuizen Th. M.
No associations
LandOfFree
Statistical thermodynamics of quantum Brownian motion: Birth of perpetuum mobile of the second kind does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Statistical thermodynamics of quantum Brownian motion: Birth of perpetuum mobile of the second kind, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistical thermodynamics of quantum Brownian motion: Birth of perpetuum mobile of the second kind will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-590147