Abstract
We formulate the statistical mechanics of chaotic system with few degrees of freedom and investigated the quartic oscillator system using microcanonical and canonical ensembles. Results of statistical mechanics are numerically verified by considering the dynamical evolution of quartic oscillator system with two degrees of freedom.
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M Bianucci, R Manella, B J West and P Grigolini, Phys. Rev. E51, 3002 (1995)
V L Berdichevsky and M V Alberti, Phys. Rev. A44, 858 (1991)
V M Bannur, P K Kaw and J C Parikh, Phys. Rev. E55, 2525 (1997)
V M Bannur, Phys. Rev. E58, 407 (1998)
H H Rugh, Phys. Rev. Lett. 78, 772 (1997)
B Hu, L Yang and Y Zhang, Phys. Rev. Lett. 97, 124302 (2006)
L Yang, P Grassberger and B Hu, Phys. Rev. E74, 062101 (2006)
G R Lee-Dadswell, B G Nickel and C G Gray, Phys. Rev. E72, 031202 (2005)
S Corezzi, M Bianucci and P Grigolini, Phys. Rev. E52, 6881 (1995)
G Casati, J Ford, F Vivaldi and W M Visscher, Phys. Rev. Lett. 52, 1861 (1984)
S Lepri, R Livi and A Politi, Phys. Rev. Lett. 78, 1896 (1997)
B Müller and T Trayanov, Phys. Rev. Lett. 68, 3387 (1992)
C Gong, Phys. Lett. B298, 257 (1993)
T S Biro, C Gong, B Müller and T Trayanov, Int. J. Mod. Phys. C5, 113 (1994)
V M Bannur, Phys. Rev. C72, 024904 (2005)
A I Khinchin, Mathematical foundations of statistical mechanics (Dover Pub., 1949)
M Lakshmanan and R Sahadevan, Phys. Rep. 224, 1 (1993)
M P Joy and M Sabir, Pramana — J. Phys. 40, 17 (1993)
M S Santhanam and J N Bandyopadhay, Phys. Rev. Lett. 95, 114101 (2005)
R K Pathria, Statistical mechanics (Butterworth-Heinemann, Oxford, 1997)
H Aiba and T Suzuki, Phys. Rev. E72, 066214 (2005)
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Bannur, V.M., Thayyullathil, R.B. Formulation of statistical mechanics for chaotic systems. Pramana - J Phys 72, 315–323 (2009). https://doi.org/10.1007/s12043-009-0027-6
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DOI: https://doi.org/10.1007/s12043-009-0027-6