You think it doesn't match because you're limiting your mental filters to the energy you've already spent in your own life. But instead lets go to someone else's house where you've not already spent one side of the energy equation. How much information do you need to find a particular pair of socks?

Indexes in a database take processing power and IOPS to generate, more than dumping it on the disk without an index. Much in the same way, taking your socks and putting them in a drawer takes more energy than dropping them at some random distance between the dryer and the drawer. But when it comes to finding the socks again use of the index (drawer) can save orders of magnitude more energy and time. In someone else's house its going to take far less information if they can point you at a particular drawer rather than you performing an exhaustive search.

There is a direct correlation here, but I won't say it's obvious as the idea that we live in an entropy driven world is a rather recent human discovery when looked at cross human history.