I'm self-studying Statistical Mechanics; in it I got Fundamental Postulate of Statistical Mechanics and that took me to ergodic hypothesis.
In the most layman's language, it says:
In an isolated system in thermal equilibrium, all microstates are equi-probable and equally-likely.
However, I could carry out my venture in Statistical Mechanics till now.
Lately, I came across the actual definition of ergodicity, especially that of Wikipedia:
[...] the term ergodic is used to describe a dynamical system which, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states (phase space).
In statistics, the term describes a random process for which the time average of one sequence of events is the same as the ensemble average.
Wikipedia writes about ergodic hypothesis:
[...] 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 ...
Also, as Arnold Neumaier wrote about ergodic hypothesis:
[...] every phase space trajectory comes arbitrarily close to every phase space point with the same values of all conserved variables as the initial point of the trajectory ....
I couldn't get those mathematical definitions as those are beyond my level; still I tried to connect these definitions with the layman's one but couldn't do so. I know a bit of phase space, ensembles and nothing more.
I would appreciate if someone explains in an intuitive manner how the definitions the time average of one sequence of events is the same as the ensemble average and 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 imply the layman's interpretation of ergodic hypothesis.