Armen E. Allahverdyan^1,2,a, Roger Balian^3,b and Theo M. Nieuwenhuizen^1,c

¹ Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.
² Yerevan Physics Institute, Alikhanian Brothers St. 2, Yerevan 375036, Armenia.
³ PhT, CEA-Saclay, 91191 Gif-sur-Yvette cedex, France.
^a [email protected]
^b [email protected]
^c [email protected]

Received: 8 August 2003 / Accepted: 30 December 2003 / 18 March 2004

Abstract: Thomson's formulation of the second law states: no work can be extracted from an equilibrium system through a cyclic process. A simple, general proof is presented for the case of macroscopic sources of work. Next the setup is generalized towards situations, where the corresponding work-source is not macroscopic. It is shown that using such a source one can extract energy from an equilibrium system by means of a cyclic process. However, this extraction is accompanied by an entropy increase of the source, in a manner resembling the Clausius inequality.

Keywords: second law; work; entropy.