Cosmic Hysteresis in Reconstructed $f(T)$ Bounce Models A Torsion-Based Thermodynamic Perspective

We investigate the emergence of cosmic hysteresis in cyclic and bouncing cosmologies within the framework of reconstructed $f(T)$ gravity. In contrast to curvature-based modifications of General Relativity, teleparallel gravity attributes gravitation to spacetime torsion encoded in the torsion scalar $T$. By reconstructing viable $f(T)$ functions corresponding to analytically prescribed nonsingular bouncing scale factors and coupling the geometry to a minimally interacting canonical scalar field, we demonstrate that asymmetric scalar field dynamics between expansion and contraction phases give rise to a non-vanishing thermodynamic work integral $\oint p_{\phi }dV$ over complete cycles. This hysteresis manifests as closed loops in the $(w_{\phi },a)$ plane, signifying thermodynamic memory and irreversibility. We derive the modified Friedmann equations, establish exact bounce and turnaround conditions, and discuss the implications of torsion-induced hysteresis for the cosmological arrow of time. Our results confirm that cosmic hysteresis is a generic feature of cyclic universes in modified gravity, extending beyond curvature-based theories.