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.
Original language | English |
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Article number | 010601 |
Journal | Physical Review Letters |
Volume | 122 |
Issue number | 1 |
DOIs | |
State | Published - 11 Jan 2019 |
Bibliographical note
Publisher Copyright:© 2019 American Physical Society.
Funding
The support of Israel Science Foundation Grant No. 1898/17 is acknowledged.
Funders | Funder number |
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Israel Science Foundation | 1898/17 |