We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of aBrownian particle to nonequilibrium oscillatory state (NOS) of Brownianparticle by considering time dependent externaldrive protocol. We consider an unbounded charged Brownian particle in thepresence of oscillatingelectric field and prove work fluctuation theorem, which is valid for anyinitial distribution and at alltimes. For harmonically bounded and constantly dragged Brownian particleconsidered by Tooru andCohen, work fluctuation theorem is valid for any initial condition(alsoNSS), but only in large timelimit. We use Onsager-Machlup Lagrangian with a constraint to obtainfrequency dependent workdistribution function, and describe entropy production rate and propertiesof dissipation functionsfor the present system using Onsager-Machlup functional.

In the causal set approach to quantum gravity, the spacetimecontinuum is replaced by a discrete substructure, the causal set, which isa locally finite poset. I will spend the first half of the talk with ageneral introduction to causal set theory. I will then discuss a 2D modelof causal set quantum gravity which overcomes the so-called entropy problemassociated with quantum geometries. In particular, 2D Minkowski spacetimeis a prediction of the theory in the large volume limit.

We outline recent advances in the quantization of noncommutativequantum field theories that preserve spacetime symmetries. This novelquantization procedure (called twisted quantization) has phenomenologicalimplications, as well as consequences for model-building in particlephysics. We explain some of these effects, like the deformation of usualspin-statistics connection at high energies.