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Thermodynamic formalism for field-driven Lorentz gases
Oliver Mülken1, Henk van Beijeren
1Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands. oliver.muelken@physik.uni-freiburg.de
Summary
We analytically determined dynamical properties of 2D field-driven Lorentz gases using thermodynamic formalism. This study provides key insights into topological and Kolmogorov-Sinai entropy for these systems.
Area of Science:
- Statistical Mechanics
- Dynamical Systems Theory
- Nonlinear Physics
Background:
- Lorentz gases are fundamental models in statistical mechanics.
- Understanding their dynamical properties is crucial for complex systems.
- Field-driven systems introduce unique behaviors.
Purpose of the Study:
- To analytically determine the dynamical properties of two-dimensional field-driven Lorentz gases.
- To calculate topological pressure and extract various entropy measures.
- To validate results against existing theoretical frameworks.
Main Methods:
- Thermodynamic formalism applied to 2D Lorentz gases.
- Isokinetic thermostat for dilute gases.
- Calculation of topological pressure up to second order in applied field strength.
- Legendre transform to define dynamical entropy.
Main Results:
- Analytic determination of topological pressure as a function of a temperature-like parameter.
- Extraction of Kolmogorov-Sinai entropy and topological entropy from dynamical entropy.
- Exact agreement of Kolmogorov-Sinai entropy with Lorentz-Boltzmann equation approach.
- Analytic results for topological entropy and calculation of the dimension spectrum.
Conclusions:
- The study successfully provides an analytical framework for understanding field-driven Lorentz gases.
- The results offer a method to calculate dimension spectra and entropy measures.
- Confirms the validity of the thermodynamic formalism for these complex systems.