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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.18344 |
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Table of Contents:
- In the study of non-equilibrium statistical mechanics, Ruelle derived explicit formulae for entropy production of smooth dynamical systems. The vanishing or strict positivity of entropy production is determined by the {\it entropy formula of folding type} \[h_μ(f)= F_μ(f)-\displaystyle\int\sum\nolimits_{λ_i(x)<0} λ_i(x)dμ(x), \] which relates the metric entropy, folding entropy and negative Lyapunov exponents. This paper establishes the formula for all inverse SRB measures of $C^{1+α}$ maps, including those with degeneracy (i.e., zero Jacobian). More specifically, we establish the equivalence that $μ$ is an inverse SRB measure if and only if the folding-type entropy formula holds and the Jacobian series is integrable. To overcome the degeneracy, we develop Pesin theory for general $C^{1+α}$ maps.