Theory reduction: The case of the kinetic theory of gases

It is often said that the kinetic theory of gases is one of the best examples of the reduction of one theory into another; that is, the classical theory of thermodynamics [or to be more exact, a significant portion of it] is alleged to be reduced to the kinetic theory, which is based on the Newtonian mechanics and the atomistic view of the matter. But what is the nature of this alleged "reduction"? If you want to know the right answer to this, the best way is to examine the historical development of the kinetic theory. The kinetic theory is a theoretical attempt to explain the nature of gases and heat processes, in general, in terms of the movements of numerous molecules constituting a gas. Its major advocates were James Clerk Maxwell (1831-79) and Ludwig Boltzmann (1844-1906); in the course of their work on the kinetic theory, they had to struggle with several conceptual problems, as well as with many empirical problems, and these conceptual problems have something to do with our question of theory reduction. And you will see that these problems center on the concept of probability. Drawing on Dr. Shin'ichiro Tomonaga's examination, I will argue that their case was not a reduction to, but an extension of, the Newtonian mechanics.
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