Constantino Tsallis
Encyclopedia
Constantino Tsallis is a naturalized Brazil
ian physicist
working in Rio de Janeiro
at CBPF, Brazil
. He was born in Greece
, and grew up in Argentina
, where he studied physics at Instituto Balseiro
, in Bariloche. In 1974 he received a Doctorat d'Etat et Sciences Physiques degree from the University of Paris-Orsay. He moved to Brazil
in 1975 with his family (his wife and daughter).
Tsallis is credited with introducing the notion of what is known as Tsallis entropy
and Tsallis statistics
in his 1988 seminal paper "Possible generalization of Boltzmann–Gibbs statistics
" published in the Journal of Statistical Physics, vol. 52, pp. 479–487. The generalization is considered to be one of the most viable and applicable candidates for formulating a theory of non-extensive
thermodynamics
. The resulting theory is not intended to replace Boltzmann–Gibbs statistics, but rather supplement it, such as in the case of anomalous systems characterised by non-ergodicity
or metastable states.
One of the most impressive experimental verifications of the predictions of q-statistic
s concerns cold atoms in dissipative optical lattices. Eric Lutz made an analytical prediction in 2003 which was verified in 2006 by a London team.
Tsallis conjectured in 1999 (Brazilian Journal of Physics 29, 1; Figure 4):
These results establish that the q-entropy provides verifiable predictions from first principles as a generalization of Boltzmann–Gibbs entropy for certain classes of phenomena.
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...
ian physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
working in Rio de Janeiro
Rio de Janeiro
Rio de Janeiro , commonly referred to simply as Rio, is the capital city of the State of Rio de Janeiro, the second largest city of Brazil, and the third largest metropolitan area and agglomeration in South America, boasting approximately 6.3 million people within the city proper, making it the 6th...
at CBPF, Brazil
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...
. He was born in Greece
Hellenic State
Hellenic State was used as the official name of the modern Greek state two times in its history:* the period of governance by Ioannis Kapodistrias in 1828–1832, when Greece was first constituted as a regular state after the Greek War of Independence * the period of Axis occupation of the country...
, and grew up in Argentina
Argentina
Argentina , officially the Argentine Republic , is the second largest country in South America by land area, after Brazil. It is constituted as a federation of 23 provinces and an autonomous city, Buenos Aires...
, where he studied physics at Instituto Balseiro
Instituto Balseiro
Balseiro Institute is an academic institution chartered by the National University of Cuyo and the National Atomic Energy Commission...
, in Bariloche. In 1974 he received a Doctorat d'Etat et Sciences Physiques degree from the University of Paris-Orsay. He moved to Brazil
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...
in 1975 with his family (his wife and daughter).
Tsallis is credited with introducing the notion of what is known as Tsallis entropy
Tsallis entropy
In physics, the Tsallis entropy is a generalization of the standard Boltzmann-Gibbs entropy. In the scientific literature, the physical relevance of the Tsallis entropy is highly debated...
and Tsallis statistics
Tsallis statistics
The term Tsallis statistics usually refers to the collection of q-analogs of mathematical functions and associated probability distributions that were originated by Constantino Tsallis. Using these tools, it is possible to derive Tsallis distributions from the optimization of the Tsallis entropic...
in his 1988 seminal paper "Possible generalization of Boltzmann–Gibbs statistics
Boltzmann entropy
In thermodynamics, specifically in statistical mechanics, the Boltzmann entropy is an approximation to the normal Gibbs entropy.The Boltzmann entropy is obtained if one assumes one can treat all the component particles of a thermodynamic system as statistically independent...
" published in the Journal of Statistical Physics, vol. 52, pp. 479–487. The generalization is considered to be one of the most viable and applicable candidates for formulating a theory of non-extensive
Intensive and extensive properties
In the physical sciences, an intensive property , is a physical property of a system that does not depend on the system size or the amount of material in the system: it is scale invariant.By contrast, an extensive property In the physical sciences, an intensive property (also called a bulk...
thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
. The resulting theory is not intended to replace Boltzmann–Gibbs statistics, but rather supplement it, such as in the case of anomalous systems characterised by non-ergodicity
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
or metastable states.
One of the most impressive experimental verifications of the predictions of q-statistic
Q-statistic
The Q-statistic is a test statistic output by either the Box-Pierce test or, in a modified version which provides better small sample properties, by the Ljung-Box test. It follows the chi-squared distribution...
s concerns cold atoms in dissipative optical lattices. Eric Lutz made an analytical prediction in 2003 which was verified in 2006 by a London team.
Tsallis conjectured in 1999 (Brazilian Journal of Physics 29, 1; Figure 4):
- That a longstanding quasi-stationary state (QSS) was expected in LONG-range interacting Hamiltonian systemHamiltonian systemIn physics and classical mechanics, a Hamiltonian system is a physical system in which forces are momentum invariant. Hamiltonian systems are studied in Hamiltonian mechanics....
s (one of the core problems of statistical mechanics). This was quickly verified by many groups around the world. - That this QSS should be described by q-statistics instead of Boltzmann–Gibbs statistics. This was verifed in June 2007 by Pluchino, Rapisarda and Tsallis (in the last figure, instead of the celebrated Maxwellian (Gaussian) distribution of velocities (valid for SHORT-range interactions), one sees a q-Gaussian).
These results establish that the q-entropy provides verifiable predictions from first principles as a generalization of Boltzmann–Gibbs entropy for certain classes of phenomena.