Large deviation theory for coin tossing and turbulence

Area of Science:

• Statistical physics
• Fluid dynamics
• Non-equilibrium systems

Background:

• Large deviations are crucial in non-equilibrium statistical physics but difficult to analyze using perturbation theory.
• The Gaussian model, typically used as a starting point for perturbation theories, is insufficient for problems dominated by large deviations, such as intermittency in fluid turbulence.

Purpose of the Study:

• To propose a novel approach for analyzing large deviations in statistical physics.
• To demonstrate the utility of a simple coin toss model as a "Gaussian model" for problems involving rare events.
• To apply this model to calculate multifractal exponents in fully developed turbulence.

Main Methods:

• Conceptualizing the coin toss distribution as a fundamental model for large deviation theory.
• Applying the coin toss model to analyze intermittency in fluid turbulence.
• Calculating multifractal exponents of order structure factors using the proposed model.

Main Results:

• The coin toss model provides an effective "Gaussian model" for understanding problems with significant rare events.
• The model facilitates the calculation of multifractal exponents in fully developed turbulence.
• This approach offers a new perspective on handling large deviations in statistical physics.

Conclusions:

• The simple coin toss distribution plays a central role in large deviation theory.
• This model is applicable to complex phenomena like intermittency in fluid turbulence.
• The proposed method advances the analysis of rare events in statistical physics and fluid dynamics.