We apply the Kolmogorov statistic to analyse the residual data of two LAGEOS satellites on General Relativistic Lense-Thirring effect, and show that it reveals a tiny difference in the properties of the satellites, possibly related to Yarkovsky-Rubin
cam effect. The recently launched LAser RElativity Satellite (LARES) can provide constraints to the extensions of General Relativity such as the Chern-Simons (CS) gravity with metric coupled to a scalar field through the Pontryagin density, so an explicit dependence on the frame dragging measurements vs the CS parameter is given.
Arrows of time - thermodynamical, cosmological, electromagnetic, quantum mechanical, psychological - are basic properties of Nature. For a quantum system-bath closed system the de-correlated initial conditions and no-memory (Markovian) dynamics are o
utlined as necessary conditions for the appearance of the thermodynamical arrow. The emergence of the arrow for the system evolving according to non-unitary dynamics due to the presence of the bath, then, is a result of limited observability, and we conjecture the arrow in the observable Universe as determined by the dark sector acting as a bath. The voids in the large scale matter distribution induce hyperbolicity of the null geodesics, with possible observational consequences.
