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arXiv · 2004.04325

Regularized Boltzmann-Gibbs statistics for a Brownian particle in a non-confining field

Lucianno Defaveri·Celia Anteneodo·David A. Kessler·Eli Barkai
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Abstract

We consider an overdamped Brownian particle subject to an asymptotically flat potential with a trap of depth $U_0$ around the origin. When the temperature is small compared to the trap depth ($\xi=k_B T/U_0 \ll 1$), there exists a range of timescales over which physical observables remain practically constant. This range can be very long, of the order of the Arrhenius factor ${\rm e}^{1/\xi}$. For these quasi-equilibrium states, the usual Boltzmann-Gibbs recipe does not work, since the partition function is divergent due to the flatness of the potential at long distances. However, we show that the standard Boltzmann-Gibbs (BG) statistical framework and thermodynamic relations can still be applied through proper regularization. This can be a valuable tool for the analysis of metastability in the non-confining potential fields that characterize a vast number of systems.

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Lucianno Defaveri, Celia Anteneodo, David A. Kessler, Eli Barkai. 2020-04-09. Regularized Boltzmann-Gibbs statistics for a Brownian particle in a non-confining field. https://doi.org/10.1103/physrevresearch.2.043088

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