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. 2016 Sep 12:6:32815.
doi: 10.1038/srep32815.

H-theorem in quantum physics

G B Lesovik  1   2 , A V Lebedev  2 , I A Sadovskyy  3 , M V Suslov  4 , V M Vinokur  3
Affiliations

H-theorem in quantum physics

G B Lesovik et al. Sci Rep. .

Abstract

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

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Figures

Figure 1
Figure 1. Scattering in a 3-lead setup.
A particle incident from the lead 1 is scattered into two other leads 2 and 3. Propagating particle induces magnetic field perpendicular to the lead direction. The spin is placed at the point where the respective fields induced by particles propagating along leads 2 and 3 are perpendicular to each other. To simplify consideration, we choose the set up design allowing to neglect the field induced by the particle in the lead 1.
Figure 2
Figure 2. Braking radiation in 1D.
(a) A scattering where electron is transmitted without photon emission. (b) A backward scattering event accompanied by the emission of photons.
Figure 3
Figure 3. 1D random walk of an electron.
Two-level systems (TLSs) shown as double well potentials are located equidistantly along the wire. Each TLS forms an effective potential for the electron, which depends on the TLS’s quantum state. For simplicity we consider a completely transparent (open) or completely reflective (closed) effective scattering potential depending on the TLS state. At each scattering event the set of TLSs is replaced by a new (unentangled) one.
Figure 4
Figure 4. Electrons and phonons in an atomic lattice.
The scattering state of an electron depends strongly on the position of the scattering atom in the lattice. Importantly, the position of the scatterer remains almost unchanged during the scattering process because of the significant mass difference between the scattered electron and the scattering atom.
See this image and copyright information in PMC

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