# Probability and Time Symmetry in Classical Markov Processes

## Abstract

Definitions of time symmetry and examples of time-directed behaviour are discussed in the framework of discrete Markov processes. It is argued that typical examples of time-directed behaviour can be described using time-symmetric transition probabilities. Some current arguments in favour of a distinction between past and future on the basis of probabilistic considerations are thereby seen to be invalid.

## Notes

### Acknowledgements

The first version of this paper was written while I was an Alexander-von-Humboldt Fellow at the Institut für Grenzgebiete der Psychologie und Psychohygiene (IGPP), Freiburg i. Br. I wish to thank in particular Werner Ehm at IGPP, Iain Martel, then at the University of Konstanz, and David Miller at the Centre for Time, University of Sydney, for useful discussions and suggestions, as well as Mauricio Suárez for the kind invitation to contribute to this volume and an anonymous referee for interesting comments.

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