Abstract
Energetics of the Undamped Stochastic Harmonic Oscillator
Highlights
Many situations in natural sciences can be successfully described in the stochastic manner [1,2,3]
Starting we focus on the undamped stochastic harmonic oscillator [27], i.e. we assume that in Eq (1) there is no damping term (−γmv(t))
To further compare analytical results with numerical approximations, we have repeated simulations for the Markovian dichotomous noise with longer correlation time, which corresponds to a smaller switching rate λ = 1/10, see Fig. 5
Summary
The harmonic oscillator is one of fundamental models in physics. In stochastic thermodynamics, such models are usually accompanied with both stochastic and damping forces, acting as energy counter-terms. On the other hand, we study properties of the undamped harmonic oscillator driven by additive noises. The popular cases of Gaussian white noise, Markovian dichotomous noise and Ornstein–Uhlenbeck noise are analyzed from the energy point of view employing both analytical and numerical methods. In accordance to one’s expectations, we confirm that energy is pumped into the system. As a function of time, initially total energy displays abrupt oscillatory changes, but transits to the linear dependence in the long-time limit. Kinetic and potential parts of the energy are found to display oscillatory dependence at all times
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