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 ...