IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v340y2004i1p309-315.html
   My bibliography  Save this article

Diffusion on fractal phase spaces and entropy production

Author

Listed:
  • Lemke, N
  • de Almeida, R.M.C

Abstract

Complex systems may show strongly non-exponential relaxation, the origins of these behavior seem to be related to the fractal structure of the phase space. In this article, we consider the diffusion on a dilute hypercube, this stochastic process is a coarse-grained model for the time evolution of a glassy system, where both the dynamics and the structure of the phase space was considered as simple as possible. We characterize this process using two quantities: a memory function and the Tsallis entropy. The first one is a measure of mixing while the second is related to non-extensivity. We characterize quantitatively their relationship. Finally, we discuss the implications for other glassy and complex systems.

Suggested Citation

  • Lemke, N & de Almeida, R.M.C, 2004. "Diffusion on fractal phase spaces and entropy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 309-315.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:309-315
    DOI: 10.1016/j.physa.2004.04.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104004297
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2004.04.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lemke, N. & de Almeida, R.M.C., 2003. "Tsallis entropy production for diffusion on the diluted hypercube," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(3), pages 396-408.
    2. Pablo G. Debenedetti & Frank H. Stillinger, 2001. "Supercooled liquids and the glass transition," Nature, Nature, vol. 410(6825), pages 259-267, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hengwei Luan & Xin Zhang & Hongyu Ding & Fei Zhang & J. H. Luan & Z. B. Jiao & Yi-Chieh Yang & Hengtong Bu & Ranbin Wang & Jialun Gu & Chunlin Shao & Qing Yu & Yang Shao & Qiaoshi Zeng & Na Chen & C. , 2022. "High-entropy induced a glass-to-glass transition in a metallic glass," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    2. Birte Riechers & Amlan Das & Eric Dufresne & Peter M. Derlet & Robert Maaß, 2024. "Intermittent cluster dynamics and temporal fractional diffusion in a bulk metallic glass," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    3. Nicole L. Mandel & Soohyun Lee & Kimyung Kim & Keewook Paeng & Laura J. Kaufman, 2022. "Single molecule demonstration of Debye–Stokes–Einstein breakdown in polystyrene near the glass transition temperature," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    4. Simone Ciarella & Dmytro Khomenko & Ludovic Berthier & Felix C. Mocanu & David R. Reichman & Camille Scalliet & Francesco Zamponi, 2023. "Finding defects in glasses through machine learning," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    5. Leo Zella & Jaeyun Moon & Takeshi Egami, 2024. "Ripples in the bottom of the potential energy landscape of metallic glass," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    6. Lars V. Bock & Helmut Grubmüller, 2022. "Effects of cryo-EM cooling on structural ensembles," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    7. Giuseppe Cassone & Fausto Martelli, 2024. "Electrofreezing of liquid water at ambient conditions," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    8. Hideaki Murase & Shunto Arai & Tatsuo Hasegawa & Kazuya Miyagawa & Kazushi Kanoda, 2023. "Spatiotemporal observation of quantum crystallization of electrons," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    9. Roger Farmer & Jean-Philippe Bouchaud, 2020. "Self-Fulfilling Prophecies, Quasi Non-Ergodicity & Wealth Inequality," NBER Working Papers 28261, National Bureau of Economic Research, Inc.
    10. Toledo-Marín, J. Quetzalcóatl & Castillo, Isaac Pérez & Naumis, Gerardo G., 2016. "Minimal cooling speed for glass transition in a simple solvable energy landscape model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 227-236.
    11. Peng Luo & Yanqin Zhai & Peter Falus & Victoria García Sakai & Monika Hartl & Maiko Kofu & Kenji Nakajima & Antonio Faraone & Y Z, 2022. "Q-dependent collective relaxation dynamics of glass-forming liquid Ca0.4K0.6(NO3)1.4 investigated by wide-angle neutron spin-echo," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    12. Sheykhali, Somaye & Darooneh, Amir Hossein & Jafari, Gholam Reza, 2020. "Partial balance in social networks with stubborn links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    13. Sebastian A. Kube & Sungwoo Sohn & Rodrigo Ojeda-Mota & Theo Evers & William Polsky & Naijia Liu & Kevin Ryan & Sean Rinehart & Yong Sun & Jan Schroers, 2022. "Compositional dependence of the fragility in metallic glass forming liquids," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    14. Robert F. Tournier & Michael I. Ojovan, 2022. "Multiple Melting Temperatures in Glass-Forming Melts," Sustainability, MDPI, vol. 14(4), pages 1-18, February.
    15. Yu Tong & Lijian Song & Yurong Gao & Longlong Fan & Fucheng Li & Yiming Yang & Guang Mo & Yanhui Liu & Xiaoxue Shui & Yan Zhang & Meng Gao & Juntao Huo & Jichao Qiao & Eloi Pineda & Jun-Qiang Wang, 2023. "Strain-driven Kovacs-like memory effect in glasses," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    16. Martinez, Luz-Maria & Angell, C.Austen, 2002. "Chemical order lifetimes in liquids, and a second fictive temperature for glassformers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 548-559.
    17. Jean-Philippe Bouchaud & Roger E. A. Farmer, 2023. "Self-Fulfilling Prophecies, Quasi Nonergodicity, and Wealth Inequality," Journal of Political Economy, University of Chicago Press, vol. 131(4), pages 947-993.
    18. Sunny Gupta & Xiaochen Yang & Gerbrand Ceder, 2023. "What dictates soft clay-like lithium superionic conductor formation from rigid salts mixture," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    19. Zhen Wei Wu & Yixiao Chen & Wei-Hua Wang & Walter Kob & Limei Xu, 2023. "Topology of vibrational modes predicts plastic events in glasses," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    20. C.N., Sachin & Joy, Ashwin, 2023. "Configurational entropy of self-propelled glass formers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:309-315. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.