%0 Book Section %1 statphys23_0709 %A Canosa, N. %A Rossignoli, R. %A Portesi, M. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K generalized majorization states statphys23 theory thermal topic-1 %T Majorization relations in generalized thermal states %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=709 %X We apply the theory of majorization to examine the rigorous disorder properties of generalized thermal distributions arising in non-extensive statistics. Majorization theory provides a notion of disorder that is stronger than that based on standard entropic relationships, which has been applied to a wide variety of fields such as economy, computer science and quantum information. In this contribution we determine the conditions that ensure the increase of the majorization based notion of disorder in such states as some parameter characterizing the distribution is increased. In particular, it is shown that if this parameter is the temperature, these conditions are satisfied by the Boltzmann-Gibbs thermal distribution as well as by the power-law distributions arising in non-extensive thermodynamic formalisms. We also show that power-law distributions have in addition a second mixing parameter related to the non-extensivity index. These properties ensure the increase of any associated entropy or disorder measure as these parameters are increased. Some illustrative results are also shown. \hfill\break 1) N. Canosa, R. Rossignoli, M. Portesi, Physica A 368 (2006) 435; Physica A 371 (2006) 126.

@incollection{statphys23_0709, abstract = {We apply the theory of majorization to examine the rigorous disorder properties of generalized thermal distributions arising in non-extensive statistics. Majorization theory provides a notion of disorder that is stronger than that based on standard entropic relationships, which has been applied to a wide variety of fields such as economy, computer science and quantum information. In this contribution we determine the conditions that ensure the increase of the majorization based notion of disorder in such states as some parameter characterizing the distribution is increased. In particular, it is shown that if this parameter is the temperature, these conditions are satisfied by the Boltzmann-Gibbs thermal distribution as well as by the power-law distributions arising in non-extensive thermodynamic formalisms. We also show that power-law distributions have in addition a second mixing parameter related to the non-extensivity index. These properties ensure the increase of {\it any} associated entropy or disorder measure as these parameters are increased. Some illustrative results are also shown. \hfill\break 1) N. Canosa, R. Rossignoli, M. Portesi, Physica A 368 (2006) 435; Physica A 371 (2006) 126.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Canosa, N. and Rossignoli, R. and Portesi, M.}, biburl = {https://www.bibsonomy.org/bibtex/2430055fbb302efe28def1772f6f2ae2a/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {cd28f03e9d3d453de4473a27ae97cd91}, intrahash = {430055fbb302efe28def1772f6f2ae2a}, keywords = {generalized majorization states statphys23 theory thermal topic-1}, month = {9-13 July}, timestamp = {2007-06-20T10:16:27.000+0200}, title = {Majorization relations in generalized thermal states}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=709}, year = 2007 }