Suppose there is an isolated system $A$ at time $(-\infty, t_1)$, whose entropy is $S=S_{max}$, i.e. it is at thermodynamical equilibrium.
Between moments $[t_1, t_2)$ the isolation is violated and system's entropy is decrased $S = S_{max} - S_d, \space\space\space 0<S_d <S_{max}$.
Question: the only way that this could happen is energy being added to system?