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## Constraints and relative entropies in nonextensive statistical mechanics (2004)

Citations: | 1 - 0 self |

### Citations

123 |
Thermodynamics of chaotic systems. An introduction. Cambridge Nonlinear
- Beck, Schlögl
- 1997
(Show Context)
Citation Context ...tatistical mechanics is the normalized q-expectation value [33], which is given by ( ) U H P nor =< > q =∑ i ε i , (1) i P i q ( pi ) = ∑ ( p j ) j q , (2) where P i is termed the escort distribution =-=[34]-=- associated with the basic distribution p i and H denotes a physical random variable (e.g., the system energy) with its ith value 2ε i . The index q is taken to be positive. However, in the literatur... |

25 | Nonextensive Statistical Mechanics and its Applications, edited by - Abe, Okamoto - 2001 |

23 | Physica A 286 - Beck - 2000 |

5 | Special issue of Physica A 305, Nos. 1/2 (2002), edited by - Kaniadakis, Lissia, et al. |

4 |
A 224, 326
- Lett
- 1997
(Show Context)
Citation Context ...ion is often used for this quantity: d x H[ p|| r] = ∑ ( pi) ( ri) dx i 1− x x→1 . (26) Kq[ p|| r] in Eq. (24) is obtained by replacing the differential operator by the Jackson qdifferential operator =-=[42]-=- x K [ p|| r] = D ∑ ( p ) ( ri) q q i i 1− x x→1 , (27) where Dq f( x) =[ f( qx) − f( x)] / [ x( q−1 )], which satisfies the q-deformed Leibniz rule D [ f( x) g( x)] =[ D f( x)] g( x) + f( x) D [ g( x... |

3 |
Physica A 322
- Taruya, Sakagami
- 2003
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Citation Context ...ganites [11], high-energy processes [1216], cosmic rays [17], cellular aggregates [18], Lévy flights [19,20], semiclassical dynamic in optical lattices [21], astrophysics and self-gravitating systems =-=[22,23]-=-, econophysical problems [24,25], kinetics of charged particles [26], Internet traffic [27], earthquakes [28,29], and complex networks [30-32] In spite of these successes, still there remain some fund... |

2 | A 273, 97 - Lett - 2000 |

2 |
e-print math-ph/0208038
- Naudts
(Show Context)
Citation Context ...Relative entropy plays a fundamental role for comparing two distributions. There exist two different kinds of the generalized relative entropies in nonextensive statistical mechanics. One is given by =-=[38]-=- I q 1 q−1 q−1 q−1 [ p|| r] = ∑ pi[ ( pi) − ( ri) ]−∑ ( pi −ri)( ri) , (23) q − 1 and the other is [39-41] K q i 1 ⎡ q [ p|| r] = − ( pi) ( ri) − q ⎢1 ∑ 1 ⎣ i 1−q i ⎤ ⎥, (24) ⎦ where r i is a referenc... |

1 |
A 67, 051402 (2003); 15 also
- Rev
- 2004
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Citation Context ...10], magnetism of colossal magnetoresistance manganites [11], high-energy processes [1216], cosmic rays [17], cellular aggregates [18], Lévy flights [19,20], semiclassical dynamic in optical lattices =-=[21]-=-, astrophysics and self-gravitating systems [22,23], econophysical problems [24,25], kinetics of charged particles [26], Internet traffic [27], earthquakes [28,29], and complex networks [30-32] In spi... |

1 |
Physica A 300, 417 (2001). See also
- Abe
- 2001
(Show Context)
Citation Context ...e that the thermodynamic Legendre-transform structure is established in both cases. However, it is still an open problem in nonextensive statistical mechanics if β is the physical inverse temperature =-=[37]-=-. It is clear that, in the limit q → 1, the Tsallis entropy in Eq. (9) tends to the Boltzmann-Gibbs-Shannon entropy S[ p] =−∑ pilnpi, and accordingly both of the distributions in Eqs. (13) and (19) co... |

1 | edited by P. Kasperkovitz and D - Abe - 1997 |