# Why Typicality Does Not Explain the Approach to Equilibrium

## Abstract

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions.

## Keywords

Lebesgue Measure Statistical Mechanic Invariant Measure Measure Zero High Entropy## Notes

### Acknowledgements

Special thanks goes to David Lavis for many illuminating discussions on SM in general, and the Boltzmannian approach in particular. I also would like to thank Craig Callender, Stephan Hartmann, Carl Hoefer, Wolfgang Pietsch, Charlotte Werndl, and two anonymous referees for valuable comments on earlier drafts. Thanks to Jean Bricmont for a helpful email conversation on his mixing condition discussed in Section 4.3, and to Detlef Dürr for drawing my attention to omissions in my first bibliography. Many thanks to Flavia Padovani for helping me with those passages in Zanghì’s chapter that were beyond the reach of my ‘FAPP Italian’. Thanks to Mauricio Suárez for organising the workshop at which this paper has first been presented, and thanks to the audiences in Madrid and Oxford for stimulating discussions. Finally, I would like to acknowledge financial support from two project grants of the Spanish Ministry of Science and Education (SB2005-0167 and HUM2005-04369).

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