de Bruijn-type identity for systems with flux

Abstract

We show that an information-theoretic relation called the de Bruijn-type identity can be reformulated in a physical context with probability currents. The time derivatives of relative entropies under the continuity equation are presented, which shows that the conservation of distance between a pair of distributions is generally not guaranteed. As an important implication of these results, we discuss and present a possible conceptual framework for the classical no-cloning (deleting) theorem and qualitatively assert that we can attribute the perfect performance of the operating machine to the openness (non-vanishing flow at boundaries between the processing machine and the system) during the process.

8 pages, no figure

References in corpus (2)

• Quantum cube: A toy model of a qubit
• Classical no-cloning theorem under Liouville dynamics by non-Csiszár f-divergence

Cited by in corpus (4)

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• Relative Fisher information in some central potentials
• Legendre transform structure and extremal properties of the relative Fisher information
• Bounds on the rates of statistical divergences and mutual information via stochastic thermodynamics