Model Systems
Model Systems
This chapter presents additional computations concerning dynamical entropy. It first computes the dynamical entropy of the quantum cat map. It then defines, for a class of non-commutative dynamical systems with a tracial invariant state, a kind of non-commutative Riemannian structure connected to Dirichlet forms that allows the definition of non-commutative Lyapunov exponents and proves Ruelle's inequality. Finally, dynamical entropy is computed for a class of quasi-free Fermionic systems. The proof exploits some ideas from scattering theory like Cook's criterion.
Keywords: Ruelle's inequality, Riemannian structure, Dirichlet form, Cook's criterion, quantum cat map
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