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Noncommutativity is an idea dating back to the early times of Quantum Mechanics and that string theory induced noncommutative (NC) geometry which provides an effective framework to study short distance spacetime dynamics. Also, string theory, a candidate for a consistent quantum theory of gravity, admits a variety of classical black hole solutions including black strings. In this paper, we study a NC geometry inspired rotating black string to cylindrical spacetime with a source given by a Gaussian distribution of mass. The resulting metric is a regular, i.e. curvaturesingularity free, rotating black string, that in large r limit interpolates Lemos [20] black string.Thermodynamical properties of the black strings are also investigated and exact expressions for the temperature, the entropy and the heat capacity are obtained. Owing to the NC correction in the solution, the thermodynamic quantities have been also modified and that the NC geometry inspired black string is always thermodynamically stable. * Electronic address:

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Employing the free energy landscape, we study the phase transition and its dynamics for a class of regular black holes in Anti-de Sitter spacetime governed by the coupling of non-linear electrodynamics, which reduces to Hayward and Bardeen solutions for particular values of spacetime parameters. The Fokker-Planck equation is solved numerically by imposing the reflecting boundary condition and a suitable initial condition, using which, we investigate the probabilistic evolution of regular AdS black holes. In this approach, the on-shell Gibbs free energy is treated as a function of the radius of the event horizon, which happens to be the order parameter of the phase transition.The numerical solution is also obtained for the absorbing boundary condition. The dynamics of switching between the coexistence small black hole phase and large black hole phase due to the thermal fluctuation is probed by calculating the first passage time. The effect of temperature on the dynamical process is also investigated.