Average entropy of a subsystem from its average Tsallis entropy

Area of Science:

• Quantum Information Theory
• Statistical Mechanics
• Non-extensive Thermodynamics

Background:

• Page's conjecture addresses the average entropy of subsystems in quantum systems.
• Standard Boltzmann-Gibbs entropy may not adequately describe all complex systems.
• The Tsallis non-extensive entropy offers an alternative framework for analyzing complex systems.

Purpose of the Study:

• To generalize Page's conjecture for subsystem entropy within the Tsallis non-extensive scenario.
• To derive the average Tsallis entropy for subsystems of a pure quantum system.
• To provide a theoretical tool for systems where standard entropy is insufficient.

Main Methods:

• Generalization of Page's conjecture using the Tsallis entropy definition.
• Consideration of a pure quantum system with Hilbert space dimension mn.
• Derivation of the average Tsallis entropy for an m-dimensional subsystem.

Main Results:

• A generalized formulation of Page's conjecture is presented for the Tsallis entropy.
• The average Tsallis entropy of an m-dimensional subsystem of a pure quantum system (dimension mn) is obtained.
• The demonstration provides a method for calculating subsystem entropy in a non-extensive context.

Conclusions:

• The generalized approach extends the understanding of subsystem entropy beyond the standard framework.
• This work offers a valuable method for analyzing complex quantum systems using Tsallis entropy.
• The findings are expected to be useful in diverse fields employing non-extensive statistical mechanics.