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Related Experiment Video

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Power fluctuation theorem for a Brownian harmonic oscillator.

J I Jiménez-Aquino¹, R M Velasco

¹Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, 09340 México, D.F., Mexico. ines@xanum.uam.mx

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

|March 19, 2013

Summary

This study validates the total power fluctuation theorem for Brownian harmonic oscillators driven out of equilibrium. The theorem holds under specific conditions, particularly in the stationary state when external colored noise is present.

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Area of Science:

Statistical Mechanics
Non-equilibrium Thermodynamics
Physics of Complex Systems

Background:

The total power fluctuation theorem is crucial for understanding energy exchange in non-equilibrium systems.
Brownian harmonic oscillators are fundamental models for studying thermal fluctuations and system dynamics.

Purpose of the Study:

To investigate the validity of the total power fluctuation theorem for a Brownian harmonic oscillator driven out of equilibrium.
To analyze the influence of different noise types (white and colored) and external fields on the theorem's applicability.

Main Methods:

Theoretical analysis of a Brownian harmonic oscillator model.
Mathematical proof of the total power fluctuation theorem under various conditions.
Consideration of systems with thermal baths, Gaussian white noise, Ornstein-Uhlenbeck processes, and electromagnetic fields.

Main Results:

The total power fluctuation theorem is proven for both ordinary and charged harmonic oscillators under different noise conditions.
The theorem's validity is demonstrated for uniform motion of the trap potential minimum.
Crucially, the theorem is shown to be valid only in the stationary state when external colored noise is applied.

Conclusions:

The total power fluctuation theorem is robust for Brownian harmonic oscillators, but its validity is sensitive to the nature of external noise.
The findings highlight the importance of considering stationary state conditions for non-equilibrium systems subjected to colored noise.