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Updated: Aug 12, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Stochastic instability of quasi-isolated systems
1Research Center for Optics and Photonics, Instituto de Fisica de São Carlos, Universidade de São Paulo, Caixa Postal 369, São Carlos, São Paulo 13560-970, Brazil.
Summary
Stochastic perturbations can destabilize dynamical systems, even if they appear stable. This stochastic instability in quasi-isolated systems explains the irreversible direction of time.
Area of Science:
- Dynamical Systems Theory
- Stochastic Processes
- Mathematical Physics
Background:
- The stability of solutions to evolution equations under perturbations is crucial in many scientific fields.
- Stochastic dynamical systems introduce randomness, complicating stability analysis.
- Asymptotic stability and stability under vanishing perturbations are key concepts.
Purpose of the Study:
- To investigate the stability of solutions to evolution equations with respect to small stochastic perturbations.
- To characterize the conditions under which a dynamical system becomes stochastically unstable.
- To explore the implications of stochastic instability for the arrow of time.
Main Methods:
- Analysis of the local stability index for stochastic dynamical systems.
- Examination of the limits of the stability index with respect to infinite time and vanishing perturbation intensity.
- Illustrative examples demonstrating the existence of destabilizing stochastic perturbations.
Main Results:
- A dynamical system is deemed stochastically unstable if the limits of its stability index do not commute.
- It is shown that for any given dynamical system, destabilizing stochastic perturbations can always be found.
- The stochastic instability of quasi-isolated systems is identified as the cause of the time's arrow irreversibility.
Conclusions:
- Stochastic perturbations can fundamentally alter the stability of dynamical systems.
- The non-commutativity of stability index limits is a definitive indicator of stochastic instability.
- Stochastic instability provides a theoretical basis for the observed irreversibility of time.
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