It is known that for a system at thermal equilibrium described by the canonical ensemble, the probability of being in a state of energy $E$ at temperature $T$ is given by the Boltzmann distribution: $$ \tag{1} P(\text{state with energy } E) \propto e^{-E/kT}. $$
I have no problems with the mathematical derivation of this result, but I do wonder if there is a way to understand what (1) means intuitively.
In other words: Is there a way to "guess" that the correct distribution for such a system is given by (1), using solely physical arguments?
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