Deriving Tsallis entropy from non-extensive Hamiltonian within a statistical mechanics framework
arXiv:2411.16757
Abstract
The Tsallis entropy, which possesses non-extensive property, is derived from the first principle employing the non-extensive Hamiltonian or the -deformed Hamiltonian with the canonical ensemble assumption in statistical mechanics. Here, the -algebra and properties of -deformed functions are extensively used throughout the derivation. Consequently, the thermodynamic quantities, e.g. internal energy and Helmholtz free energy, are derived and they inheritly exhibit the non-extensiveness. From this intriguing connection between Tasllis entropy and the -deformed Hamiltonian, the parameter encapsulates the intrinsic degree of non-extensivity for the thermodynamic systems.
21 pages, 1 figure