One of the crucial properties of the Boltzmann-Gibbs entropy in the context of classical thermodynamics is extensivity, namely proportionality with the number of elements of the system. The Boltzmann-Gibbs entropy satisfies this prescription if the subsystems are statistically (quasi-) independent, or typically if the correlations within the system are essentially local. In such cases the energ...

Equilibrium or meta-equilibrium incomplete thermostatistics with different q indices Abstract We discuss a possibility of establishing a nonextensive incomplete statistics based on Tsallis entropy for equilibrium systems with different q values.

ISSN: 2186-1390 http://www.ijcvsp.com Abstract In this paper, a fuzzy approach for image segmentation based on Tsallis entropy is introduced. This approach employs fuzzy Tsallis entropy to measure the structural information of image and to locate the optimal threshold desired by segmentation. The proposed method draws upon the postulation that the optimal threshold concurs with maximum informat...

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving co...

Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized q-average energy Abstract Tsallis' thermostatistics with the standard linear average energy is revisited by employing S 2−q , which is the Tsallis entropy with q replaced by 2 − q. We explore the connections among the S 2−q approach and the other different versions of Tsal-lis ...

It is demonstrated clearly that for the same classical generalized system the Tsallis power-laws with both the 1 > q and the 1 < q can be induced by the constraint of the constant harmonic mean for the so-called reciprocal energies r E and at the same time the Boltzmann distribution or the negative exponential probability distribution can be generated with the constraint of the constant arithme...

Image segmentation is a significant step in image analysis and computer vision. Many entropy based approaches have been presented in this topic; among them, Tsallis entropy is one of the best performing methods. However, 1D Tsallis entropy does not consider make use of the spatial correlation information within the neighborhood results might be ruined by noise. Therefore, 2D Tsallis entropy is ...

We give bounds on the difference between weighted arithmetic mean and geometric mean. These imply refined Young inequalities reverses of inequality. also study some properties Applying newly obtained inequalities, we show results Tsallis divergence, R\'{e}nyi Jeffreys-Tsallis divergence Jensen-Shannon-Tsallis divergence.

We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes’ inequality.

In a previous paper (1) it was shown how, for a dynamical system, the probability distribution function of the sojourn–times in phase–space, defined in terms of the dynamical orbits (up to a given observation time), induces unambiguously a statistical ensemble in phase–space. In the present paper it is shown which is the p.d.f. of the sojourn–times corresponding to a Tsallis ensemble (this, by ...