已知函数\(f\left ( {x} \right )=\left \{ \begin{gathered} {\frac {1} {e}\left ( {x+2} \right )，x<1} \\ {\ln {x，x>1}} \end{gathered} \right .\) ，若 \(f\left( {{x_1}} \right) = f\left( {{x_2}} \right)\) 且 \({x_2} > {x_1}\) ，则 \({x_2} - {x_1}\) 的最小值为___.

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