Nonextensive entropy
Encyclopedia
Entropy
is considered to be an extensive property, i.e., that its value depends on the amount of material present. Constantino Tsallis
has proposed a nonextensive entropy, which is a generalization of the traditional Boltzmann-Gibbs entropy.
The rationale behind the theory is that Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality most materials behave quite independently of initial conditions.
Nonextensive entropy leads to nonextensive statistical mechanics
, whose typical functions are power law
s, instead of the traditional exponential
s.
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
is considered to be an extensive property, i.e., that its value depends on the amount of material present. Constantino Tsallis
Constantino Tsallis
Constantino Tsallis is a naturalized Brazilian 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...
has proposed a nonextensive entropy, which is a generalization of the traditional Boltzmann-Gibbs entropy.
The rationale behind the theory is that Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality most materials behave quite independently of initial conditions.
Nonextensive entropy leads to nonextensive statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, whose typical functions are power law
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
s, instead of the traditional exponential
Exponential
Exponential may refer to any of several mathematical topics related to exponentiation, including:*Exponential function, also:**Matrix exponential, the matrix analogue to the above*Exponential decay, decrease at a rate proportional to value...
s.