  We straight-forwardly derive the Onsager-Machlup Lagrangian from the
Fokker-Planck equation and show that friction and dissipation are a natural
property of the equation of motion. We develop a method to calculate the local
variance $\sigma_{2}\,b(q)^{2}$ and identify this function as a
Helmholtz-factor. In both meanings the function $b(q)$ describes properties of
the environment. For application, we examine the free fall through a barometric
medium and model a blow of wind by a solitonic pulse running through the
medium. We treat harmonic oscillators immersed in a thermal bath, finding
intuitive as well as counter-intuitive phenomena of friction. By allowing the
temperature to be time-dependent, the dynamical process of cooling and heating
becomes self-consistently available. We find a state of dynamical balance
between system and environment. Last, we show that dynamical balance is related
to adiabatic thermodynamic processes. In a special case, dynamical balance can
induce a real phase-transition.
