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Tsallis thermostatistics for finite systems: a Hamiltonian approach

Author

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  • Adib, Artur B.
  • Moreira, André A.
  • Andrade Jr, José S.
  • Almeida, Murilo P.

Abstract

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann–Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi–Pasta–Ulam chain of anharmonic oscillators.

Suggested Citation

  • Adib, Artur B. & Moreira, André A. & Andrade Jr, José S. & Almeida, Murilo P., 2003. "Tsallis thermostatistics for finite systems: a Hamiltonian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 276-284.
    • Handle: RePEc:eee:phsmap:v:322:y:2003:i:c:p:276-284
    DOI: 10.1016/S0378-4371(02)01601-1
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    Cited by:

    1. Vignat, C. & Plastino, A., 2006. "Poincaré's observation and the origin of Tsallis generalized canonical distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 167-172.
    2. Tsallis, Constantino & Borges, Ernesto P. & Plastino, Angel R., 2023. "Entropy evolution at generic power-law edge of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Dunkel, Jörn & Hilbert, Stefan, 2006. "Phase transitions in small systems: Microcanonical vs. canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 390-406.

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