Ising ferromagnet and nonadditive entropies: equilibrium and nonequilibrium properties

Some equilibrium and nonequilibrium properties of the one-dimensional nearest-neighbor Ising ferromagnet that are grounded on nonadditive entropies are reviewed. First, we focus on the known fact that the nonadditive entropy $$S_q$$ S q for a special value of q, namely $$q^\star =\sqrt{37}-6 \simeq 0.0828$$ q ⋆ = 37 - 6 ≃ 0.0828 , yields entropic extensivity, thus satisfying the Legendre structure of classical thermodynamics, at the quantum critical point of the spin-1/2 ferromagnetic Ising chain in the presence of an external transverse field. Then we address a well-known issue in phase transitions, namely that, at the critical point, quantities such as the susceptibility and the Grüneisen ratio diverge within Boltzmann–Gibbs statistical mechanics ( $$q=1$$ q = 1 ). Moreover, we show that such thermostatistical quantities diverge for $$q>q^\star $$ q > q ⋆ , vanish for $$q