Entropy à la Boltzmann

Jayanta K Bhattacharjee is Professor of theoretical physics at the Indian Association for the Cultivation of Science. His research interests lie in problems in statistical physics and nonlinear dynamics.

A discussion of entropy after the life and times of Boltzmann must of necessity be anachronistic [1]. Entropy historically was introduced in the early study of thermodynamics, a science which brought together the previously unrelated mechanical and thermal energies. Thermodynamics was robust enough to survive the two great revolutions of the early twentieth century -- the theory of relativity and the quantum theory. Consequently, it might seem natural to stay with thermodynamics and introduce entropy from that standpoint. Thermodynamics is a practical science based on physical arguuments, and has its genesis in efforts to understand the efficiencies of various engines, which were devices that converted thermal energy to mechanical energy. However, it is also true that thermodynamics is a fairly abstract [2] science and the introduction of entropy from the thermodynamic point of view cannot be immediately visualized via a physical picture. Paradoxically it is the Boltzmann picture, which was little understood and even less believed in Boltzmann's lifetime, which is somewhat more physically accessible. This is to a large extent because the molecular picture to which Boltzmann appealed constantly is today much better understood and established beyond doubt. In contrast, the molecular picture was not universally accepted in the latter half of the nineteenth century and it was impossible for Boltzmann's contemporaries to appreciate his point of view. However, after the developments of the twentieth century, it is more normal to approach entropy from the Boltzmann view [3] and that is what we will try to do.

Read full article (177  Kb)

Address for Correspondence
Jayanta K Bhattacharjee Department of Theoretical Physics, 
Indian Association for the 
Cultivation of Science, 
Jadavpur, Calcutta 700032, India. 
Email: tpjkb@iacs.ernet.in