ENTROPY AND PROBABILITY 6lthe first to state that the second law is statistical in nature.* In a letter about his
'demons,' probably written early in 1868, he discussed their naming, their char-
acteristics, and their purpose:'1. Who gave them this name? Thompson.**
- What were they by nature? Very small but lively beings incapable of doing
work but able to open and shut valves which move without friction or inertia. - What was their chief end? To show that the 2nd Law of Thermodynamics
was only a statistical certainty.. .' [M2].
Boltzmann had already begun his attempts to derive the second law when Max-
well wrote these lines, but he did not yet understand its statistical character. The
stated purpose of Boltzmann's first paper on the subject (1866) was 'to give a
completely general proof of the second law of the theory of heat, as well as to
discover the theorem in mechanics that corresponds to it' [B2].f He made a fresh
start when he returned to the problem in 1871-2: 'The problems of the mechan-
ical theory of heat are. .. problems in the theory of probability' [B3]. His new
proof was based on the so-called kinetic method [E3, K3]. In the first of two
papers, he dealt with the equilibrium relation between entropy, heat, and tem-
perature [B4]. The sequel, published in 1872 [B3], is one of his most important
papers. It contains the Boltzmann equation. It also contains the H theorem: there
exists a quantity, later called //, defined in terms of the velocity distribution, with
the property that dH/dt < 0 so that, up to a negative multiplicative constant, H
can be identified with the entropy. Both mechanical and probabilistic arguments
are used in the derivation of this theorem. (In that same period, Boltzmann also
did important work on the equipartition theorem and in 1876 gave the derivation
of the 'law' of Dulong and Petit. The discussion of equipartition and of specific
heats will be deferred to Chapter 20.)
At that time, Boltzmann still did not have it entirely straight, however. He
believed that he had shown that the second law is absolute, that H can never
increase. He made the final step as the result of his reflections^: on a remark by
Johann Joseph Loschmidt [L4] which in modern terms can be phrased as follows.
Consider a large number of particles moving according to fully specified initial
conditions and subject to the standard time-reversal invariant Newtonian laws.
'Maxwell's views on the second law are discussed in more detail by Klein [K2].
**This is William Thomson, later Baron Kelvin of Largs. In December 1867, Maxwell had written
a letter to Peter Guthrie Tail in which he introduced 'a finite being who knows the path and veloc-
ities of all the molecules by simple inspection' [Ml]. Tail had shown this letter to Thomson, who
invented the name demon for Maxwell's finite being.fA quite similar attempt was made by Clausius in 1871 [C3]. This led to a priority argument
between Boltzmann and Clausius—to the amusement of Maxwell [K2].
$ For the influence of Loschmidt's ideas on Boltzmann, see especially [K3].
t