In textbooks on statistical mechanics, one finds often arguments based on
classical mechanics, phase space and ergodicity in order to justify the second
law of thermodynamics. However, the basic equations of motion of classical
mechanics are deterministic and reversible, while the second law of
thermodynamics is irreversible and not deterministic, because it states that a
system forgets its past when approaching equilibrium. I argue that all
"derivations" of the second law of thermodynamics from classical mechanics
include additional assumptions that are not part of classical mechanics. The
same holds for Boltzmann's H-theorem. Furthermore, I argue that the
coarse-graining of phase-space that is used when deriving the second law cannot
be viewed as an expression of our ignorance of the details of the microscopic
state of the system, but reflects the fact that the state of a system is fully
specified by using only a finite number of bits, as implied by the concept of
entropy, which is related to the number of different microstates that a closed
system can have. While quantum mechanics, as described by the Schroedinger
equation, puts this latter statement on a firm ground, it cannot explain the
irreversibility and stochasticity inherent in the second law.Comment: Invited talk given on the 2012 "March meeting" of the German Physical
Society To appear in: B. Falkenburg and M. Morrison (eds.), Why more is
different (Springer Verlag, 2014