End of the universe

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

Before 1981, the universe had already past 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 continue to feed entropy from our universe into E-Space. (DW: Logopolis)

The end of the Universe has been 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 figure given in The Infinity Doctors was likely a result of the continued existence of the Time Lords. When they were destroyed in the Last Great Time War, it may have shortened the lifespan of the universe.

The universe will end sometime around the year 100,000,000,000,000 when the galaxies collapse and all the great civilisations have died out. (DW:  Utopia)

The 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: Special Occasions: 2. Do You Love Anyone Enough?)