Scattering approach to the thermodynamics of quantum transport

Pierre Gaspard

doi:10.1088/1367-2630/17/4/045001

Abstract

The thermodynamic entropy production for the scattering processes of noninteracting bosons and fermions in mesoscopic systems is shown to be related to the difference between the Connes–Narnhofer–Thirring entropy per unit time, characterizing temporal disorder in the motion of quantum particles, and the associated time-reversed coentropy per unit time. Under nonequilibrium conditions, the positivity of thermodynamic entropy production can thus be interpreted as a time-reversal symmetry breaking in the temporal disorder of the quantum transport process. Moreover, the full counting statistics of both fermionic and bosonic quantum transport is formulated in relation with the energy and particle currents producing thermodynamic entropy in nonequilibrium steady states.

Highlights

At positive temperature, atoms and molecules undergo ceaseless collisions and their motion is highly irregular, manifesting fluctuations on micrometric and nanometric spatial scales, as illustrated with Brownian motion
A scattering approach to the thermodynamics of quantum transport is developed for noninteracting bosons or fermions in small open systems
The scattering approach is formulated in terms of the scattering matrix, which allows us to describe the quantum coherent dynamics of noninteracting bosons or fermions flowing across the open system

Summary

INTRODUCTION

Atoms and molecules undergo ceaseless collisions and their motion is highly irregular, manifesting fluctuations on micrometric and nanometric spatial scales, as illustrated with Brownian motion. For stochastic processes such as Brownian motion or Markovian jump processes, the ( , τ )-entropy per unit time increases with the resolution as → 0 or τ → 0 and it can be experimentally measured from time series [11, 12] Such dynamical large-deviation quantities allow us to characterize the chaotic properties of temporal disorder in different types of stochastic systems [13,14,15]. It is shown that entropy production in the flow of noninteracting fermions or bosons can be expressed in terms of the time asymmetry in the nonequilibrium temporal disorder characterized by the CNT entropy per unit time and its associated coentropy.

Scattering in a mesoscopic circuit

Temporal disorder in the forward and reversed processes

Thermodynamic entropy production

Full counting statistics and entropy production

TRANSPORT OF BOSONS

CONCLUSIONS