This law follows simply from statistics: if a physical system is given (is allowed to occupy) new energy states which are equivalent to the existing states (say, a gas is expanding into a larger volume), then the system will occupy "new" states on equal footing with the existing ("old") ones.
For thermodynamics, a thermodynamic state of a system is fully identified by values of a suitable set of parameters known as state variables, state parameters or thermodynamic variables.
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Phase transition, the transformation from one thermodynamic state to another.