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Fluctuation theorem for a single particle in a moving billiard: experiments and simulations
Malte Schmick1, Qi Liu, Qi Ouyang
1Max-Planck-Institut für molekulare Physiologie, Postfach 500247, 44202 Dortmund, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
A single driven particle in a Sinai billiard system verifies the fluctuation theorem (FT). Chaoticity is tunable, but the FT fails with unstable orbits at low restitution coefficients.
Area of Science:
- Statistical mechanics
- Dynamical systems
Background:
- The fluctuation theorem (FT) is a key concept in non-equilibrium statistical mechanics, describing the statistical properties of entropy production in systems driven far from equilibrium.
- Sinai billiard systems, known for their chaotic dynamics, provide a model for studying fundamental principles in statistical physics.
Purpose of the Study:
- To experimentally and computationally investigate whether a single driven particle in a Sinai billiard-like system is sufficient to observe the fluctuation theorem (FT).
- To explore the relationship between system chaoticity, controlled by the restitution coefficient, and the validity of the FT.
Main Methods:
- Experimental tracking of a single particle in a periodically driven Sinai-billiard-like setup.
- Hard-sphere molecular dynamics simulations to model the particle's behavior.
- Systematic variation of the restitution coefficient to adjust the degree of chaoticity.
Main Results:
- Both experimental and simulation results confirmed the validity of the fluctuation theorem (FT) with a single driven particle.
- The chaoticity of the system was successfully tuned by altering the restitution coefficient of collisions.
- The FT was observed to break down when unstable periodic orbits emerged, particularly at small restitution coefficients.
Conclusions:
- A single driven particle is sufficient to demonstrate the fluctuation theorem (FT) in this Sinai billiard system.
- The restitution coefficient serves as an effective parameter to control system chaoticity and its impact on the FT.
- The emergence of unstable periodic orbits signifies a regime where the FT is no longer applicable.
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