ABSTRACT

This chapter discusses some mathematical aspects of thermodynamics. It explores interesting structures like Jacobian matrices and their determinants called Jacobians. The chapter introduces the powerful notions of differential forms and their properties. These provide extremely compact codifications of the various laws of thermodynamics. The chapter illustrates the powerfulness of Jacobians by showing the equivalence of the four Maxwell relations to a single Jacobian condition. It provides examples of their use in thermodynamics. The chapter shows that while all these mathematical techniques enable one to derive results known earlier in compact, succinct and elegant ways, they do not really add anything significant towards a deeper physical understanding of thermodynamics. The chapter offers very powerful techniques which should be part of the ’armory’ of any serious student of thermodynamics.