Abstract
Given an equilibrium state µ for a continuous function f on a shift of finite type X, the pressure of f is the integral, with respect to µ, of the sum of f and the information function of µ. We show that under certain assumptions on f, X and an invariant measure ν, the pressure of f can also be represented as the integral with respect to ν of the same integrand. Under stronger hypotheses we show that this representation holds for all invariant measures ν. We establish an algorithmic implication for approximation of pressure, and we relate our results to a result in thermodynamic formalism.
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Marcus, B., Pavlov, R. An integral representation for topological pressure in terms of conditional probabilities. Isr. J. Math. 207, 395–433 (2015). https://doi.org/10.1007/s11856-015-1178-4
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DOI: https://doi.org/10.1007/s11856-015-1178-4