In the algebraic quantum theory we know a few properties characterising equilibrium states. These are KMS-condition, stability and passivity. Passivity is the property suggested by second law of thermodynamics. By definition a quantum system is in a passive state if it is unable to perform a work in any cyclic adiabatic process. I shall give mathematical formulation of this property and discuss its implications. In particular the relation between passivity and KMS-condition will be discussed. As an application the famous Carnot formula for the efficiency of heat engines will be derived. (Based on a joint paper with W. Pusz)