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Results tagged with ergodicity
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user 115736
A system is said to be ergodic if time averages are, for a sufficient long time, equivalent to phase space averages. This "ergodic hypothesis" is taken by many authors as the foundation of statistical mechanics.
3
votes
Relation between ergodic hypothesis and fundamental postulate of statistical mechanics?
Ergodic hypothesis (EH): Over long periods of time, the time spent by a system in some region of the phase space of microstates with the same
energy is proportional to the volume of this region.
…
- 16.5k
19
votes
Accepted
Why does the Coarse-grained Entropy increase?
The probability density $\rho(p(t),q(t))$ of an Hamiltonian system follows Liouville's equation:
$$\frac{d\rho}{dt}=0 \tag{1}\label{1}$$
The intuitive interpretation of \ref{1} is that the probabili …
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1
vote
Microcanonical ensemble, ergodicity and symmetry breaking
For such systems, we cannot even tell if ergodicity is really broken or if the time that we must wait for the system to thermalize is simply too large for us to measure. … This means that if $N$ is "large enough" $\tau$ will be longer than the age of the universe and therefore the system will have, for any practical purpose, broken ergodicity. …
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