I've left my computer unattended with Minecraft open for quite a few hours (game was paused), and returned to find excessive resource usage from Minecraft, at times the FPS counter reported high framerates (75 - 140 FPS) but was displaying clearly choppy output.
From running a clean copy of the game, (without changing the amount of allocated RAM) the game's allocated memory seems to zig-zag up and down wildly, but keeps increasing by about 3-20Mb every round. This persists until the game crashes.

What I expected to happen was...:
I expected that coming back to the computer, I would continue where I left off, and the computer being usable.

What actually happened was...:
The game had choppy video, after a few minutes chunks stopped loading as I was "stranded" on a section of land, and a few minutes later my framerate dropped below 5, and shortly after, the game crashed.

Note:
The game did not use more than 93% of it's allocated memory.
3297Mb / 3533Mb, before the crash it fluctuated between 3292 and 3297 but never over.

Steps to Reproduce:
1. Allocate 4Gb RAM to Minecraft
2. Open the game and load a creative mode map
3. Let the game run for a few hours (about 10)
4. Continue playing until game crashes, and computer resource usage spikes to unplayable levels