## Scattering theory and thermodynamics of quantum transport.(English)Zbl 1337.82018

The purpose of the present article is to explain how the time-reversal symmetry of Hamiltonian microdynamics can be compatible with the thermodynamic time asymmetry. There the key issue is that the equations of motion may have solutions that do not share the symmetry of the equations. The symmetry breaking takes place at the statistical level of description due to the fact that forward and time reversed paths have different probabilities under nonequilibrium condictions. Temporal disorder, as it occurs in scattering processes, can be characterized by the concept of $$\epsilon$$-entropy per unit time [P. Gaspard and X.-J. Wang, “Noise, chaos, and $$(\varepsilon, \tau)$$ entropy per unit time”, Phys. Rep. 235, No. 6, 291–343 (1993; doi:10.1016/0370-1573(93)90012-3)]. This concept was generalized to quantum systems by Connes, Narnhofer, and Thirring. It allows to describe temporal disorder in many-body quantum systems of fermions and bosons (see [A. Connes et al., Commun. Math. Phys. 112, 691–719 (1987; Zbl 0637.46073)]; [H. Narnhofer and W. Thirring, Lett. Math. Phys. 14, 89–96 (1987; Zbl 0628.46065)]). Here, the theory is applied to study the scattering theory in open systems, where scattering particles may also randomly arrive from surrounding reservoirs.
From the abstract: “Scattering theory is complemented by recent results on full counting statistics, the multivariate fluctuation relation for currents, and time asymmetry in temporal disorder characterized by the Connes-Narnhofer-Thirring entropy per unit time, in order to establish relationships with the thermodynamics of quantum transport. Fluctuations in the bosonic or fermionic currents flowing across an open system in contact with particle reservoirs are described by their cumulant generating function, which obeys the multivariate fluctuation relation as the consequence of microreversibility. Time asymmetry in temporal disorder is shown to manifest itself out of equilibrium in the difference between a time-reversed coentropy and the Connes-Narnhofer-Thirring entropy per unit time. The difference is shown to be equal to the thermodynamic entropy production for ideal quantum gases of bosons and fermions. The results are illustrated for a two-terminal circuit.”

### MSC:

 82C70 Transport processes in time-dependent statistical mechanics 81U05 $$2$$-body potential quantum scattering theory

### Citations:

Zbl 0637.46073; Zbl 0628.46065
Full Text:

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