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Fluctuation relations with intermittent non-Gaussian variables.

Adrián A Budini¹

¹Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche, Avenida E Bustillo Km 9.5, 8400 Bariloche, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 7, 2012

Summary

This study reveals that subtracting two independent random variables, one a modulated Poisson process, naturally satisfies fluctuation relations (FRs) in nonequilibrium systems. This demonstrates the compatibility of intermittency and FRs, offering insights into non-Gaussian fluctuations.

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Area of Science:

Statistical Mechanics
Non-equilibrium Physics
Stochastic Processes

Background:

Nonequilibrium stationary fluctuations can exhibit fluctuation relations (FRs), a special symmetry.
Understanding the conditions under which FRs hold is crucial for nonequilibrium statistical mechanics.

Purpose of the Study:

To demonstrate that fluctuation relations (FRs) are satisfied by the subtraction of two independent random variables under a thermodynamic-like change of measure.
To show the compatibility of intermittency and FRs in nonequilibrium systems.
To analyze the non-Gaussian features of probability distributions and their large deviation functions.

Main Methods:

Modeling the system as the subtraction of two independent random variables.
Utilizing a modulated Poisson process as one of the random variables.
Analyzing the probability distribution, generating function, and large deviation functions.

Main Results:

The subtraction of two independent random variables related by a thermodynamic-like change of measure inherently satisfies fluctuation relations (FRs).
Intermittency and FRs are shown to be compatible and can coexist naturally.
Strong non-Gaussian features are observed in the probability distribution and its generating function.
Large deviation functions exhibit a characteristic 'kink' at the origin and a plateau regime.

Conclusions:

The proposed model provides a framework for understanding systems exhibiting both intermittency and fluctuation relations.
The findings have potential applications in various stationary nonequilibrium situations.
The study highlights the importance of non-Gaussian statistics in describing complex nonequilibrium phenomena.