Quantum Kolmogorov-Sinai entropy and Pesin relation

• URL: http://arxiv.org/abs/2010.06068v2
• Date: Wed, 31 Mar 2021 16:05:12 GMT
• Title: Quantum Kolmogorov-Sinai entropy and Pesin relation
• Authors: Tomer Goldfriend and Jorge Kurchan
• Abstract summary: A quantum Kolmogorov-Sinai entropy is defined as the entropy production per unit time resulting from coupling the system to a weak, auxiliary bath. We show a quantum (Pesin) relation between this entropy and the sum of positive eigenvalues of a matrix describing phase-space expansion.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss a quantum Kolmogorov-Sinai entropy defined as the entropy production per unit time resulting from coupling the system to a weak, auxiliary bath. The expressions we obtain are fully quantum, but require that the system is such that there is a separation between the Ehrenfest and the correlation timescales. We show that they reduce to the classical definition in the semiclassical limit, one instance where this separation holds. We show a quantum (Pesin) relation between this entropy and the sum of positive eigenvalues of a matrix describing phase-space expansion. Generalizations to the case where entropy grows sublinearly with time are possible.

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