The ergodic hypothesis is also important for the Boltzmann approach.
2.
The ergodic hypothesis is often assumed in the statistical analysis of computational physics.
3.
The ergodic hypothesis is not a necessary condition for statistical mechanics to work.
4.
The concepts of ergodicity and the ergodic hypothesis are central to applications of ergodic theory.
5.
The assumption can be made by invoking the ergodic hypothesis as well as the Hamiltonian systems.
6.
In physics the term is used to imply that a system satisfies the ergodic hypothesis of thermodynamics.
7.
Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the heat bath.
8.
But Liouville's theorem does " not " imply that the ergodic hypothesis holds for all Hamiltonian systems.
9.
A statistical mechanical system in equilibrium can be modeled, via the ergodic hypothesis, as the stationary distribution of a stochastic process.
10.
However, using the ergodic hypothesis, the temperature can still be obtained to arbitrary precision by further averaging the momenta over a long enough time.
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