By Robert Huggins

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As a result, the temporal symmetry of the theory is broken. Irreversibility appears as a result of the scission of the unitary group describing the evolution into two dissipative, nonunitary semigroups. 7) Prigogine states quite rightly: ‘‘An extension of dynamics? This appears as a very strong statement, that can easily be misunderstood. There is no question here about adding new terms to the equations of dynamics. . ’’ ‘‘. . There is no question of adding new terms that would break the symmetry of the equations, like Epicurus’ clinamen.

Thus, information is lost in going from r to Ãr; but this loss is much subtler than the one produced in any ‘‘coarse graining’’ operations, performed in the ‘‘traditional’’ treatments of statistical mechanics. ’’ y On the basis of the properties discussed above, the authors prove that Wt , though being defined for all t, can only preserve positivity for t > 0, or for t < 0, but not for both together. Thus, the passage to the stochastic description implies the breaking of the time symmetry: The initial group of unitary y transformations Ut splits up into two distinct contracting semigroups Wt : for t > 0 and for t < 0.

Bogoliubov, and the Dutch school directed by G. Uhlenbeck) worked independently in the same direction; the results always turned out to be equivalent. Prigogine was always in the forefront: A proof is the large number of foreign visitors, co-workers, and students he attracted. ’’ E. ’’ He begins a collaboration with his colleague (and also former disciple of De Donder) Jules Ge´ he´ niau and with two younger physicists (Edgard Gunzig and Pasquale Nardone) in the field of cosmology. Einstein’s equations of general relativity led to the celebrated model (initially due to the Belgian abbotphysicist Georges Lemaıˆtre) of the ‘‘Big bang,’’ known today even by children.

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