ZT represents a symmetry, and the stronger objection (2) of above means that there are far more solutions with dB / dt ~ O. Any definition of entropy as a state functional with F(z) -I- F(ZT) would introduce an absolute direction in time. In order to understand the thermodynamical arrow of time, one has to explain the kaltgeburt (or simply to postulate it in some specific form). The Second Law is therefore not incompatible with deterministic or T -symmetric dynamical laws, although it is extremely improbable (and therefore in conflict with statistical reasoning) in every theory with an unchanging set of 'potential' states.

1 Derivation of Classical Master Equations 47 coll ision Fig. 1. Transformation of information about particle momenta into information about correlations between them as the basis of the H-theorem. the distance of the Sirius would completely change the microscopic state of a gas within seconds. Although the deviations in the paths of the individual molecules caused by this difference is extremely small, the resulting difference of the momenta is amplified in each collision by a factor of the order of l/ R, the ratio of the mean free path over the molecular radius.

Then its time-reversed orbit ZT( -t) == {qi( -t), -Pie -t)} is a solution of the The technical simplification of this argument by assuming an exact T-symmetry of the laws of nature has occasionally misled to the by no means justified expectation that the difficulty in deriving the Second Law may be overcome simply by dropping this symmetry. 34 3. The Thermodynamical Arrow of Time equations of motion too. In quantum mechanics, z(t) == 'ljJ(t) is Schrodinger's wave function, and ZT( -t) == 'ljJ* (-t) is Wigner's time-reversal transformation.