Energetics of the single-well undamped stochastic oscillators

Abstract

The paper discusses analytical and numerical results for non-harmonic, undamped, single-well, stochastic oscillators driven by additive noises. It focuses on average kinetic, potential and total energies together with the corresponding distributions under random drivings, involving Gaussian white, Ornstein-Uhlenbeck and Markovian dichotomous noises. It demonstrates that insensitivity of the average total energy to the single-well potential type, $V(x)\propto x^{2n}$, under Gaussian white noise does not extend to other noise types. Nevertheless, in the long-time limit ($t\to \infty$), the average energies grow as power-law with exponents dependent on the steepness of the potential $n$. Another special limit corresponds to $n\to \infty$, i.e. to the infinite rectangular potential well, when the average total energy grows as a power-law with the same exponent for all considered noise types.

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References in corpus (3)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Fluctuation theorems for harmonic oscillators
• Mass Dependence of Instabilities of an Oscillator with Multiplicative and Additive Noise

Cited by in corpus (1)

• Bounding energy growth in friction-less stochastic oscillators