No-pumping theorem for non-Arrhenius rates |
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| Institution: | 1. Humanitas College, Kyung Hee University, Yongin 17104, Republic of Korea;2. Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea;1. Department of Cardiology, University Hospital Basel, Switzerland;2. Cardiovascular Research Institute Basel (CRIB), University Hospital Basel, Switzerland;3. Division of Nuclear Medicine, University Hospital Basel, Switzerland;4. Department of Laboratory Medicine, University Hospital Basel, Switzerland;1. Biomedical Research and Innovation Platform, South African Medical Research Council, Cape Town, South Africa;2. Division of Chemical Pathology, Faculty of Medicine and Health Sciences, National Health Laboratory Service (NHLS) and University of Stellenbosch, Cape Town, South Africa;3. Non-Communicable Diseases Research Unit, South African Medical Research Council, Cape Town, South Africa;4. Department of Medicine, University of Cape Town, Cape Town, South Africa;5. Department of Biomedical Sciences, Faculty of Health and Wellness Sciences, Cape Peninsula University of Technology, Cape Town, South Africa;1. Laboratoire LEREC, Département de Physique, Faculté des Sciences, Université Badji Mokhtar, Annaba, Algeria;2. Laboratoire LPR, Département de Physique, Faculté des Sciences, Université Badji Mokhtar, Annaba, Algeria;3. Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;4. Laboratoire de Physique Quantique et de Modélisation Mathématique (LPQ3M), Département de Technologie, Université de Mascara, 29000 Mascara, Algeria |
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| Abstract: | The no-pumping theorem refers to a Markov system that holds the detailed balance, but is subject to a time-periodic external field. It states that the time-averaged probability currents nullify in the steady periodic (Floquet) state, provided that the Markov system holds the Arrhenius transition rates. This makes an analogy between features of steady periodic and equilibrium states, because in the latter situation all probability currents vanish explicitly. However, the assumption on the Arrhenius rates is fairly specific, and it need not be met in applications. Here a new mechanism is identified for the no-pumping theorem, which holds for symmetric time-periodic external fields and the so called destination rates. These rates are the ones that lead to the locally equilibrium form of the master equation, where dissipative effects are proportional to the difference between the actual probability and the equilibrium (Gibbsian) one. The mechanism also leads to an approximate no-pumping theorem for the Fokker-Planck rates that relate to the discrete-space Fokker-Planck equation. |
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