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Relaxation-speed crossover in anharmonic potentials.

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Thermal relaxation in anharmonic potentials can be faster during heating or cooling. A new phase diagram reveals how initial temperatures and potential anharmonicity dictate these relaxation speeds.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Previous research observed faster thermal relaxation during heating than cooling in specific systems.
  • Understanding thermal relaxation dynamics is crucial in various physical phenomena.

Purpose of the Study:

  • To investigate the conditions under which thermal relaxation can exhibit faster heating or cooling.
  • To map the parameter space governing these relaxation behaviors in anharmonic potentials.

Main Methods:

  • Analysis of overdamped diffusion in anharmonic potentials.
  • Development of a relaxation-speed phase diagram based on initial temperatures and potential anharmonicity.

Main Results:

  • Overdamped diffusion in anharmonic potentials generically shows both faster heating and faster cooling.
  • A phase diagram identifies distinct regions for faster heating, faster cooling, and a crossover behavior.
  • Heating can be initially slower but asymptotically faster than cooling in a specific crossover region.

Conclusions:

  • The observed relaxation dynamics are dependent on initial temperatures and the degree of potential anharmonicity.
  • The findings are robust to the inclusion of harmonic terms and variations in temperature measures.
  • This work provides a comprehensive understanding of thermal relaxation asymmetries in anharmonic systems.