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Convergence to the Asymptotic Large Deviation Limit.

Maxime Debiossac1, Nikolai Kiesel1, Eric Lutz2

  • 1<a href="https://ror.org/03prydq77">University of Vienna</a>, Faculty of Physics, VCQ, Boltzmanngasse 5, A-1090 Vienna, Austria.

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Summary
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We experimentally investigated large deviation theory for a levitated nanoparticle. Singular prefactors were found to significantly restrict convergence to the asymptotic limit, offering new insights into rare event dynamics.

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Area of Science:

  • Statistical physics
  • Non-equilibrium thermodynamics
  • Experimental physics

Background:

  • Large deviation theory provides a framework for studying rare events in dynamical systems.
  • Experimental applications are often limited by finite statistics, hindering access to asymptotic regimes.
  • Understanding convergence is crucial for applying theoretical models to real-world data.

Purpose of the Study:

  • To experimentally investigate the large deviation properties of stochastic work and heat.
  • To determine the convergence domain of large deviation estimators without prior knowledge of probability distributions.
  • To analyze the impact of singular prefactors on convergence characteristics.

Main Methods:

  • Utilized a levitated nanoparticle system subjected to non-equilibrium feedback control.
  • Applied a novel criterion to assess the convergence domain of large deviation estimators.
  • Extracted both asymptotic exponential decay and subexponential prefactors for analysis.

Main Results:

  • Demonstrated that singular prefactors significantly restrict convergence to the asymptotic large deviation limit.
  • Quantified the convergence domain of estimators for stochastic work and heat.
  • Identified the critical role of prefactors in the approach to the asymptotic regime.

Conclusions:

  • Singular prefactors play a pivotal role in limiting the convergence of large deviation estimators.
  • The study provides unique experimental insights into the approach to the asymptotic large deviation limit.
  • The findings advance the experimental application of large deviation theory to complex systems.