Universality of heat and entropy transport in 1D channels at arbitrary temperatures

Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering “Horia Hulubei” 407 Atomiştilor street, P.O. BOX MG-6, Magurele, Jud. Ilfov, Romania, EU

^a dragos@theory.nipne.ro

Received: 20 February 2011
Accepted: 9 May 2011

Abstract

I show that there is a close analogy between the quantities that describe one-dimensional (1D) quantum transport and the thermodynamic quantities of 2D quantum gases at equilibrium; for example the particle, energy, heat and entropy fluxes are analogous to the particle number, internal energy, heat capacity and entropy, respectively. Based on this, I write analytic expressions for the transport quantities and I show that the heat conductivity and entropy current are independent of statistics at any temperature. The quanta of heat conductance is therefore the low-temperature limit of the heat conductance of one channel and is the same —as expected from the analogy above— as the low-temperature limit of heat capacity. The physical interpretation of this remarkable universality of 1D transport is given in terms of configurations of particle populations which carry the same heat fluxes.