What's harder: Shuffling a sorted deck or sorting a shuffled one?
By Landauer's principle, if you want to take a uniform random permutation of $n$ keys to a sorted one, and not keep any bits in the computer which reveal what the uniform random permutation was, you need to erase $log n! \approx n \log_2 n$ bits. This will take $(n \ln n) k T$ energy. On the other hand, the computation taking the sorted array and $n \log_2 n$ random bits to the random array is reversible, and thus the energy expended can be made arbitrarily small.

Note that these are just theoretical lower bounds. The energy currently consumed by these processes on an actual digital computer bears no relation to the above analysis.