End of the universe

The end of the Universe, known to the Time Lords as "Event Two" and to others as the "Big Crunch", was an event that would take place far off into the future where the universe, or N-Space, collapsed in on itself due to two factors: the universe was a closed system; and the constant build-up of entropy.

Before 1981, the universe had already passed the point of collapse. Having discovered this, the Logopolitans created Charged Vacuum Emboitments which opened N-Space into another universe, E-Space, allowing entropy into E-Space. Though Logopolis was destroyed in 1981, the CVEs were rebooted and still continued to feed entropy from our universe into E-Space. (DW: Logopolis)

The Panjistri created the God Machine in an attempt to prevent the end of the Universe. (NA: Timewyrm: Apocalypse)

The end of the Universe was projected to occur in varied times, including the years 60,000,000,000 AD (BFA: Zagreus), 100,000,000,000,000 AD (DW: Utopia) and 100,000,000,000,000,000,000,000,000,000,000 (One hundred nonillion) AD. (PDA: The Infinity Doctors)

The Fourth Doctor and Romana watched the Universe end from some unknown vantage point. As the dimensions collapsed, the Doctor gave Romana the last Rolo in the Universe. (ST: Do You Love Anyone Enough?)