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On the foundations of statistical mechanics: ergodicity, many degrees of freedom and inference | | Sergio Chibbaro
; Lamberto Rondoni
; Angelo Vulpiani
; | | Date: |
1 Oct 2014 | | Abstract: | The present paper is meant to give a simple introduction to the problem of
the connection between microscopic dynamics and statistical laws. For sake of
simplicity, we mostly refer to non-dissipative dynamics, since dissipation adds
technical difficulties to the conceptual issues, although part of our
discussion extends beyond this limit. In particular, the relevance of chaos and
ergodicity is here confronted with that of the large number of degrees of
freedom. In Section 2, we review the microscopic connection, along the lines of
Boltzmann’s approach, and of its further developments. In Section 3, we discuss
the falsifiability of statistical mechanics and its role as statistical
inference. In particular we argue that the Maximum entropy priciple is in
general not a predictive tool. | | Source: | arXiv, 1410.0223 | | Services: | Forum | Review | PDF | Favorites | |
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