Abstract
A geometrical description of the virial theorem (VT) of statistical mechanics is presented using the symplectic formalism. The character of the Clausius virial function is determined for second-order differential equations of the Liénard type. The explicit dependence of the virial function on the Jacobi last multiplier is illustrated. The latter displays a dual role, namely, as a position-dependent mass term and as an appropriate measure in the geometrical context.
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Acknowledgements
The authors are extremely thankful and grateful to other collaborators, Manuel F Rañada, Fernando Falceto and Irina Gheorghiu, in this project for their valuable discussions. Authors are also grateful to referee for the comments and valuable suggestions. Partial financial support by the research projects MTMÐ2012/33575 (MINECO, Madrid) and DGA-E24/1 (DGA, Zaragoza) is acknowledged. Finally, and most importantly, PG acknowledges the efficient, friendly, considerate and professional assistance he received from the organizing members of the PNLD 2013 meeting.
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CARIÑENA, J.F., CHOUDHURY, A.G. & GUHA, P. Generalized virial theorem for the Liénard-type systems. Pramana - J Phys 84, 373–385 (2015). https://doi.org/10.1007/s12043-014-0925-0
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DOI: https://doi.org/10.1007/s12043-014-0925-0