The Samsung Galaxy S6 has a Close All option when you open the Recent apps. While it isn't necessary to close these, I wonder what amount of memory would be consumed if a year or more goes by without cleaning up the Recent apps tray?
While this is sort of a backwards question, as it implies that you want to use less memory (which while true in Windows, is not true in Linux and Android), I don't think the number would be very large. The system is always going to be using some RAM to do its background processing and the ideal situation is for it to use as much as possible to either hold apps in RAM or be able to front load the runtime processes and have just enough left over to fluidly facilitate dynamic switching between threads when the use switches tasks (ie, returns to home, opens a new app). Android will automatically free up whatever resources it needs in order to seamlessly accomplish these tasks - and it will do so with what it believes to be an optimal ratio of working vs ready RAM.
If we make the assumption that a person is going to open any given app approximately X times per day - it is definitely less RAM intensive (and less resource intensive overall) for the app to be held in RAM and re-accessed without having to start it up anew each time. While ART (Android Run Time) does take some of this inefficiency out of the equation by doing much of the processing the first time an app is installed/accessed (and accessed per boot), there is still an efficiency loss when closing an app and reopening it versus freezing it and reopening it. Most apps are meant to behave in the dynamic resource management environment and can misbehave when constantly closed and re-opened - which makes users think that they need to "restart it" by closing and reopening it and/or rebooting - and the cycle continues. Letting things handle themselves is much better.
And again, the recent apps tray isn't a list of open or "cached" apps, it is a list of apps that have been opened recently. Clicking on one does one of two things: 1. If the app was recently opened and is still held in RAM, it will be re-opened where you left off. 2. If the app was closed by the dynamic resource allocation processes, it will open the app. Both of these actions take place exactly in the same manner as if you clicked on the icon from the home screen or app drawer - unless you have taken action to close the app otherwise (back out of apps that code for that, selecting exit from a menu, force closing it, etc).