The present work is motivated by the study of reference [1], where the generalized second law (GSL) of thermodynamics has been investigated for a flat FRW universe for three viable models of f (T ) gravity. We have here considered a non-flat universe and, accordingly, studied the behaviors of equation of state (EoS) parameter ω and of the deceleration parameter q.Subsequently, using the first law of thermodynamics, we derived the expressions for the time derivative of the total entropy of a universe enveloped by apparent horizon. In the next phase, with the choice of scale factor a (t) pertaining to an emergent universe, we have investigated the sign of the time derivatives of total entropy for the models of f (T ) gravity considered.

We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.

This work is motivated by the work of Kim et al. (Mod. Phys. Lett. A 23:3049, 2008), which considered the equation of state parameter for the new agegraphic dark energy based on generalized uncertainty principle coexisting with dark matter without interaction. In this work, we have considered the same dark energy interacting with dark matter in emergent, intermediate and logamediate scenarios of the universe. Also, we have investigated the statefinder, kerk and lerk parameters in all three scenarios under this interaction. The energy density and pressure for the new agegraphic dark energy based on generalized uncertainty principle have been calculated and their behaviors have been investigated. The evolution of the equation of state parameter has been analyzed in the interacting and non-interacting situations in all the three scenarios. The graphical analysis shows that the dark energy behaves like quintessence era for logamediate expansion and phantom era for emergent and intermediate expansions of the universe.

We investigate the most general form of the one-dimensional Dirac Hamiltonian HD in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we construct a quasi-Hamiltonian K, defined as the square of HD, to explore the consequences. We show that the diagonal elements of K under a suitable approximation reflect the presence of a superpotential, thus proving a useful guide in unveiling the role of SUSY. For illustrative purposes, we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.

We study the thermodynamics of the apparent, event and particle horizons in this modified gravity. We observe that under this gravity, the time derivative of total entropy stays at positive level and hence the generalized second law is validated.