Tsallis entropy

Tsallis entropy is a non-extensive generalization of Shannon entropy introduced by Constantino Tsallis in 1988. Unlike Shannon entropy, which is additive across independent subsystems, Tsallis entropy is pseudo-additive: the entropy of a composite system depends on a parameter q that characterizes the degree of non-extensivity. This property makes it a candidate framework for systems with long-range interactions, memory effects, or multifractal structure — phenomena that conventional statistical mechanics struggles to capture.

The formula for Tsallis entropy is:

S_q = (1/(q−1)) (1 − Σ pᵢ^q)

As q → 1, Tsallis entropy recovers Shannon entropy. For q > 1, it penalizes rare events more heavily; for q < 1, it weights them more generously. The physical interpretation of q remains contested: some researchers treat it as a fitting parameter, others as a fundamental constant of the system under study. Whether Tsallis entropy represents a genuine extension of thermodynamics or merely a flexible curve-fitting tool is an open question in non-extensive statistical mechanics.