From Non-Normalizable Boltzmann-Gibbs Statistics to Infinite-Ergodic Theory

Erez Aghion, David A. Kessler, and Eli Barkai
Phys. Rev. Lett. 122, 010601 – Published 3 January 2019
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Abstract

We study a particle immersed in a heat bath, in the presence of an external force which decays at least as rapidly as 1/x, e.g., a particle interacting with a surface through a Lennard-Jones or a logarithmic potential. As time increases, our system approaches a non-normalizable Boltzmann state. We study observables, such as the energy, which are integrable with respect to this asymptotic thermal state, calculating both time and ensemble averages. We derive a useful canonical-like ensemble which is defined out of equilibrium, using a maximum entropy principle, where the constraints are normalization, finite averaged energy, and a mean-squared displacement which increases linearly with time. Our work merges infinite-ergodic theory with Boltzmann-Gibbs statistics, thus extending the scope of the latter while shedding new light on the concept of ergodicity.

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  • Received 17 April 2018
  • Revised 30 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.010601

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsGeneral Physics

Authors & Affiliations

Erez Aghion1,2,*, David A. Kessler1, and Eli Barkai1,2

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
  • 2Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel

  • *Corresponding author. ErezAgh5@gmail.com

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Issue

Vol. 122, Iss. 1 — 11 January 2019

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