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Tsallis thermostatistics for finite systems: a Hamiltonian approach

Artur B. Adib·Andre A. Moreira·Jose S. Andrade Jr.·Murilo P. Almeida
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Abstract

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.

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Artur B. Adib, Andre A. Moreira, Jose S. Andrade Jr., Murilo P. Almeida. 2002-08-14. Tsallis thermostatistics for finite systems: a Hamiltonian approach. https://doi.org/10.1016/s0378-4371(02)01601-1

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