Abstract
A first-principles derivation is presented of canonical distributions for a finite thermostat taking into account nonextensive energy. Parameterizing this energy by λ, we derive an explicit form for the distribution functions by regulating λ, and then explore the nontrivial relationship between these functions and energy nonextensivity, as well other system parameters such as system size. A variational entropy function is also derived from these distribution functions..
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Combes F, Robert R, Pfenniger D, et al. Statistical mechanics of non-extensive systems. C R Phys, 2006, 7: 307–470
Wang R, Nganso D S, Kaabouchi E A, et al. Investigation of an energy nonadditivity for nonextensive system. Chinese Sci Bull, 2011, 56, doi: 10.1007/s11434-011-4676-8
Wang L N, Min J C. Thermodynamic analysis of adsorption process at a non-equilibrium steady state. Chinese Sci Bull, 2010, 55: 3619–3625
Shao Y Z, Zhong W R, He Z H. Nonequilibrium dynamic transition in a kinetic Ising model driven by both deterministic modulation and correlated stochastic noises. Chinese Sci Bull, 2005, 50: 2422–2426
Almeida M P. Thermodynamical entropy (and its additivity) within generalized thermodynamics. Physica A, 2003, 325: 426–438
Adib A B, Moreira A A, Andrade J S, et al. Tsallis thermostatistics for finite systems: A Hamiltonian approach. Physica A, 2003, 322: 276–284
Gross D H E. Phase transitions in “small” systems — A challenge for thermodynamics. Nuclear Phys A, 2001, 681: 366–373
Plastino A R, Plastino A. From Gibbs microcanonical ensemble to Tsallis generalized canonical distribution. Phys Lett A, 1994, 193: 140–143
Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys, 1988, 52: 479–487
Abe S, Rajagopal A K. Rivisting disorder and Tsallis statistics. Science, 2003, 300: 249–250
Ou C J, Chen J C. Thermostatistic properties of a q-generalized Bose system trapped in an n-dimensional harmonic oscillator potential. Phys Rev E, 2003, 68: 026123
Du J L. The nonextensive parameter and Tsallis distribution for self-gravitating systems. Europhys Lett, 2004, 67: 893–899
Ou C J, Chen J C, Wang Q A. Temperature definition and fundamental thermodynamic relations in incomplete statistics. Chaos Soliton Fract, 2006, 28: 518–521
Ou C J, Chen J C. Two long-standing problems in Tsallis’ statistics. Physica A, 2006, 370: 525–529
Wang Q A. Incomplete statistics: Nonextensive generalizations of statistical mechanics. Chaos Soliton Fract, 2001, 12: 1431–1437
Wang Q A. Nonextensive statistics and incomplete information. Eur Phys J B, 2002, 26: 357–368
Wang Q A, Nivanen L, Mehaute A L, et al. Temperature and pressure in nonextensive statistics. Europhys Lett, 2004, 65: 606–612
Ou C J, Li W, Du J, et al. Possible canonical distributions for finite systems with nonadditive energy. Physica A, 2008, 387: 5761–5767
Terletski Y P. Statistical Physics. Amsterdam: North-Holland, 1971
Abe S. General pseudoadditivity of composable entropy prescribed by the existence of equilibrium. Phys Rev E, 2001, 63: 061105
Li W, Wang Q A, Nivanen L, et al. On different q-systems in nonextensive thermostatistics. Eur Phys J B, 2005, 48: 95–100
Wang Q A. Probability distribution and entropy as a measure of uncertainty. J Phys A Math Theor, 2008, 41: 065004
Abe S, Martinez S, Pennini F, et al. Classical gas in nonextensive optimal Lagrange multipliers formalism. Phys Lett A, 2001, 278: 249–254
Wang X D, Kang S. Application of polynomial chaos on numerical simulation of stochastic cavity flow. Sci China Tech Sci, 2010, 53: 2853–2861
Zhang Y M, Huang X Z, Zhang X F, et al. System reliability analysis for kinematic performance of planar mechanisms. Chinese Sci Bull, 2009, 54: 2464–2469
Li H X. Probability representations of fuzzy systems. Sci China Ser F-Inf Sci, 2006, 49: 339–363
Liu D F, Wen S Q, Wang L P. Poisson-Gumbel mixed compound distribution and its application. Chinese Sci Bull, 2002, 47: 1901–1906
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Zheng, L., Li, W. Thermoequilibrium statistics for a finite system with energy nonextensivity. Chin. Sci. Bull. 56, 3666–3670 (2011). https://doi.org/10.1007/s11434-011-4726-2
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DOI: https://doi.org/10.1007/s11434-011-4726-2