On the second law of thermodynamics I. General framework

Abstract

In this paper a general framework for discussing the classical statements of the second law of thermodynamics is developed. The thermodynamic systems with which the theory deals need not obey the first law and can undergo general (not necessarily quasi-static) processes. By using the formalism of heat distribution measures introduced in previous papers of the author, the classical verbal statements are converted into meaningful mathematical conditions. These conditions can be put into a general form which is the same for all the classical statements. The main result of the paper is an abstract theorem which shows that the general condition leads to one or two inequalities for cyclic processes. In the subsequent part of the paper the abstract theorem is applied to the specific conditions corresponding to the classical statements of the second law. The number of the corresponding inequalities depends on the condition in question, but in each case these inequalities are generalization of the Clausius inequality to which they reduce if the first law holds. By comparing the inequalities corresponding to various statements of the second law also the relations among the statements are established in the second part of the paper.