Eur. Phys. J. B (2013) 86: 363
https://doi.org/10.1140/epjb/e2013-40634-9

Regular Article

de Bruijn-type identity for systems with flux

Department of Mathematics and Physics, Faculty of Science, Kanagawa University, 2946, 6-233 Tsuchiya, Hiratsuka, 259-1293 Kanagawa, Japan

^a e-mail: yamano@amy.hi-ho.ne.jp

Received: 30 June 2013
Received in final form: 17 July 2013
Published online: 28 August 2013

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.