In Stochastic Thermodynamics, heat is a random variable with probability distribution associated. Studies of the are mostly in overdamped regime and one dimension. Here we solve underdamped for three different cases: free particle, linear potential, harmonic potential. All them arbitrary dimensions. The results exact generalize known literature.

Exact Langevin equations are derived for the height fluctuations of surfaces driven by the deposition of material from a molecular beam. We consider two types of model: deposition models, where growth proceeds by the deposition and instantaneous local relaxation of particles, with no subsequent movement, and models with concurrent random deposition and surface diffusion. Starting from a Chapman...

We study a class of optimal stochastic control problems arising from the control of movements. Exact solutions are first presented for linear cases for both the duringand post-movement control problem, depending on a parameter α > 0. It is found that for the Langevin type equation and for the post-movement control case, a non-degenerate solution exists only when α > 1/2. For the Langevin type e...