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Chaos, Dynamics, and Fractals by Joseph L. McCauley

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8

Statistical mechanics on symbol sequences

8.1  Introduction to statistical mechanics

In the last chapter, we found that the fractal dimension can be understood as the ratio of a Boltzmann entropy to a corresponding Liapunov exponent. We also met and used a certain Legendre transform that reminds us of thermodynamics. Are these results accidental, or are they the sign of a deeper analogy that we have yet to explore?

Let us begin with the statistical equilibrium of a chaotic dynamical system for the special case where the distribution of iterates is even over the natural coarsegraining: is the frequency with which the interval is visited. Then ...

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