Eur. Phys. J. B 64, 105-118 (2008)
https://doi.org/10.1140/epjb/e2008-00270-2

Quantum thermodynamic processes: a control theory for machine cycles

¹ Chair for Theoretical Physics and Applied Mathematics, Urals State Technical University, Mira 19, 620002 Jekaterinburg, Russia
² Institut für Theoretische Physik 1, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

Corresponding author: ^a jan.birjukow@daad-alumni.de

Received: 8 November 2007
Revised: 20 May 2008
Published online: 9 July 2008

Abstract

The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this 2-dimensional control plane. Putting aside coherence we show that for a large class of quantum objects with discrete spectra and for the cycles considered the Carnot efficiency applies as a universal upper bound. In the dynamic (finite time) regime renormalized thermodynamic variables allow to include non-equilibrium phenomena in a systematic way. The machine function ceases to exist in the large speed limit; the way, in which this limit is reached, depends on the type of cycle considered.