Eur. Phys. J. D 62, 67-71 (2011)
https://doi.org/10.1140/epjd/e2010-00270-9

Stochastic dynamics, efficiency and sustainable power production

¹ Université Pierre et Marie Curie, Département de Mathémathiques, Tour 16, Boîte 121, 75252 Paris Cedex 05, France
² Université Pierre et Marie Curie-CNRS, LPTMC (UMR 7600), Boîte 121, 75252 Paris Cedex 05, France
³ Clarkson University, Dept of Physics, Potsdam, 13699-5820 NY, USA

^a e-mail: moreau@lptl.jussieu.fr

Received: 15 May 2010
Received in final form: 14 September 2010
Published online: 5 November 2010

Abstract

In the framework of stochastic thermodynamics, we give a precise expression of power dissipation in a heat engine, and study the relation between entropy and power dissipation. Using these relations, we propose a reasonable and general definition of efficiency for thermal engines in a non-equilibrium stationary state. This definition, different from Carnot efficiency, seems appropriate to the concerns of sustainable development. We show that non-zero dissipation is necessary for producing non-vanishing power. Furthermore, close to equilibrium and even in much broader situations, when power production is maximum with respect to relevant variables the power dissipation is at less equal to the power delivered to a mechanical, external system, and the corresponding “sustainable efficiency” is at most ½. From this result, we deduce a new upper bound for Carnot efficiency at maximum power. It is compared to similar, but different upper bounds obtained previously by other authors.