q-analog - Tsallis Q-theory

Tsallis Q-theory

As an application, In Tsallis' q-theory, one begins by defining the q-addition of two real numbers:

Q-addition is commutative, associative, has 0 as the identity element, and for q=1 becomes the usual sum of x and y. By inversion, q-subtraction is defined:

The q-product is defined as:

where is defined to mean x when and 0 when . Note that for, q-division by zero is allowed. By inversion, q-division is defined as:

Many q-functions may be defined using the above building blocks, such as the Tsallis q-exponential and its inverse, the Tsallis q-logarithm which are defined as:

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q-analog - Tsallis Q-theory
... As an application, In Tsallis' q-theory, one begins by defining the q-addition of two real numbers Q-addition is commutative, associative, has 0 as the identity element, and for q=1 becomes the usual sum of x and y ... defined using the above building blocks, such as the Tsallis q-exponential and its inverse, the Tsallis q-logarithm which are defined as ...