Dynamical Systems and Microphysics pp 155-165 | Cite as

# Reversibility Versus Irreversibility in the Physical Universe

## Abstract

What do we mean when we say that the laws of physics are time-reversible? There is an immediate answer: if in the mathematical expression of physical laws, we change t into — t, then we get the same system or an equivalent one. This purely formal criterion needs some clarification. Let us suppose that the considered law is expressed as a differential system. In general, this system is not of first order (more frequently of second order). By introducing new variables (in general put equal to first order derivatives), the p-variables,one gets a new differential system of first order: a flow defined in a manifold M (phase space) by a vector field X. We may define the same flow in the product M × ℝ of M by the time axis ℝ. Then time reversibility can be expressed as follows.

## Keywords

Phase Space Modular Space Hamiltonian Formalism Unitary Formalism Physical Universe## Preview

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## References

- [1]Avez, A.,
*Méthodes ergodiques en Mécanique classique*, (part on Return spectrum of a rotation), Gauthiers-Villars 1966.Google Scholar - [2]Théorème de S. Newhouse, in Abraham R., Narsden J. Foundations of Mechanics Benjamin 1978 (second edition).Google Scholar
- [3]Thom R.,
*Stabilité structurelle et Morphogenese*chap. V. Benjamin 1972.Google Scholar - [4]see [3] and Thom R. Analysis and catastrophes, Proceedings International Congress of Semantics, Vienna June 1979, to appear.Google Scholar
- [5]Thom R., L’espace et la réalité physique, Orbetello Congress of the International Academy of Sciences, April 1979, Agazzi ed.Google Scholar