On the relationship between the Fisher-Frieden-Soffer arrow of time,and the behaviour of the Boltzmann and Kullback entropies |
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| Institution: | 1. Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina;2. Department of Physics, University of Pretoria, Pretoria 0002, South Africa;1. Neuroscience Program, Jacobs School of Medicine and Biomedical Sciences, State University of New York at Buffalo, Buffalo, NY;2. Child and Family Asthma Studies Center, Oishei Children''s Hospital, Buffalo, NY;3. Department of Pediatrics, Jacobs School of Medicine and Biomedical Sciences, State University of New York at Buffalo, Buffalo, NY;4. Allergy & Immunology, Oishei Children''s Hospital, Buffalo, NY;5. Department of Psychiatry, Jacobs School of Medicine and Biomedical Sciences, State University of New York at Buffalo, Buffalo, NY;1. Neurology Department, Hospital São Sebastião, CHEDV, Santa Maria da Feira, Portugal;2. Clinical Research Office, Health Sciences Department (SACS), University of Aveiro, Portugal;3. Institute of Electronics and Telematics Engineering of Aveiro (IEETA), University of Aveiro, Portugal;4. University Institute of Maia – ISMAI, Maia, Portugal;5. Rehabilitation Medicine Department, Hospital São Sebastião, CHEDV, Santa Maria da Feira, Portugal;6. UnIGENe, Instituto de Biologia Molecular e Celular, University of Porto, Portugal;1. Vrije Universiteit Brussel, Faculty of Physical Education and Physiotherapy, Pleinlaan 2, 1050 Brussel, Belgium;2. Vrije Universiteit Brussel, Faculty of Sciences and Bio-engineering, Pleinlaan 2, 1050 Brussel, Belgium;3. Universiteit Antwerpen, Faculty of Applied Engineering, Groenenborgerlaan 171, 2020 Antwerpen, Belgium;4. Thim Van Der Laan University College Physiotherapy, Weststrasse 8, 7302 Landquart, Switzerland;1. Qiushi Academy for Advanced Studies, Zhejiang University, Hangzhou 310027, China;2. Key Laboratory of Biomedical Engineering of Ministry of Education, Zhejiang University, Hangzhou 310027, China;3. Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China;4. Zhejiang Provincial Key Laboratory of Cardio-Cerebral Vascular Detection Technology and Medicinal Effectiveness Appraisal, Zhejiang University, Hangzhou 310027, China;5. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shengzhen 518055, China;1. Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain;2. Departamento de Física Aplicada II, Escuela Técnica Superior de Ingeniería de Edificación, Universidad de Sevilla, 41012 Sevilla, Spain;3. Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain;4. Departamento de Física Aplicada, EINA, Universidad de Zaragoza, 50018 Zaragoza, Spain |
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| Abstract: | We provide a new derivation of the H-theorem satisfied by Fisher's information measure (I) for the diffusion equation and show that the ensuing monotonically decreasing behaviour of I yields, in turn, an H-theorem involving the second time derivative of the standard Boltzmann-Gibbs-Shannon entropy S. An upper bound for S(t) is obtained from this latter relation. Additionally, it is demonstrated that, under certain conditions, the behaviour of I may be related to that of the relative information measure of Kullback. This latter result is generalized to the case of the Fokker-Planck equation. |
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