CHAPTER 4 THE SECOND LAW
4.8 THESTATISTICALINTERPRETATION OFENTROPY 131
of statistical mechanics, the results for an isolated system are derived with a microcanonical
ensemble, and for a system of constant temperature with a canonical ensemble.
A changeÅSstatof the statistical entropy function given by Eq.4.8.1is the same as the
changeÅSof the macroscopic second-law entropy, because the derivation of Eq.4.8.1is
based on the macroscopic relation dSstatD∂q=TD.dU ∂w/=Twith dUand∂wgiven
by statistical theory. If the integration constantCis set equal to zero,Sstatbecomes the
third-law entropySto be described in Chap. 6.
Equation4.8.1shows that a reversible process in which entropy increases is accom-
panied by an increase in the number of accessible microstates of equal, or nearly equal,
internal energies. This interpretation of entropy increase has been described as the spread-
ing and sharing of energy^11 and as the dispersal of energy.^12 It has even been proposed
that entropy should be thought of as a “spreading function” with its symbolSsuggesting
spreading.13,14
(^11) Ref. [ 100 ].
(^12) Ref. [ 96 ].
(^13) Ref. [ 97 ].
(^14) The symbolSfor entropy seems originally to have been an arbitrary choice by Clausius; see Ref. [ 82 ].