### Abstract

The existence and exact form of the continuum expression of the discrete nonlogarithmic q-entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic q-entropy is irrelevant for the continuous classical systems. In this work, we show how the discrete nonlogarithmic q-entropy in fact converges in the continuous limit and the negative of the q-entropy with continuous variables is demonstrated to lead to the (Csiszár type) q-relative entropy just as the relation between the continuous Boltzmann-Gibbs expression and the Kullback-Leibler relative entropy. As a result, we conclude that there is no obstacle for the applicability of the q-entropy to the continuous classical physical systems.

Original language | English |
---|---|

Article number | 012104 |

Journal | Physical Review E |

Volume | 97 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 5 2018 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E*,

*97*(1), [012104]. https://doi.org/10.1103/PhysRevE.97.012104

**Route from discreteness to the continuum for the Tsallis q -entropy.** / Oikonomou, Thomas; Bagci, G. Baris.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 97, no. 1, 012104. https://doi.org/10.1103/PhysRevE.97.012104

}

TY - JOUR

T1 - Route from discreteness to the continuum for the Tsallis q -entropy

AU - Oikonomou, Thomas

AU - Bagci, G. Baris

PY - 2018/1/5

Y1 - 2018/1/5

N2 - The existence and exact form of the continuum expression of the discrete nonlogarithmic q-entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic q-entropy is irrelevant for the continuous classical systems. In this work, we show how the discrete nonlogarithmic q-entropy in fact converges in the continuous limit and the negative of the q-entropy with continuous variables is demonstrated to lead to the (Csiszár type) q-relative entropy just as the relation between the continuous Boltzmann-Gibbs expression and the Kullback-Leibler relative entropy. As a result, we conclude that there is no obstacle for the applicability of the q-entropy to the continuous classical physical systems.

AB - The existence and exact form of the continuum expression of the discrete nonlogarithmic q-entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic q-entropy is irrelevant for the continuous classical systems. In this work, we show how the discrete nonlogarithmic q-entropy in fact converges in the continuous limit and the negative of the q-entropy with continuous variables is demonstrated to lead to the (Csiszár type) q-relative entropy just as the relation between the continuous Boltzmann-Gibbs expression and the Kullback-Leibler relative entropy. As a result, we conclude that there is no obstacle for the applicability of the q-entropy to the continuous classical physical systems.

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UR - http://www.scopus.com/inward/citedby.url?scp=85040173250&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.97.012104

DO - 10.1103/PhysRevE.97.012104

M3 - Article

VL - 97

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 1

M1 - 012104

ER -