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Entropy, a product of the second law of thermodynamics, was the slow, irreversible process of breakdown and decay whereby a complex, organised system inevitably degraded into more chaotic ones.
After being driven by the Chronovore Artemis (PROSE: No Future) to the alternative universe of the Silurian Earth, the Seventh Doctor explained that the only force capable of invading a TARDIS was the primal force of the universe itself, the entropy of time. (PROSE: Blood Heat) According to him "entropy gets to us all, in the end ... people and computers and empires", (PROSE: Original Sin) even chocolate wrappers. In entropy, nothing was indestructible, (PROSE: This Town Will Never Let Us Go) and everything had its end. (PROSE: Original Sin)
Being a complex and energetic closed system, N-Space, the main universe, had a finite lifespan and would have "died" some time prior to the 20th century had the Logopolitans not vented entropy from it into E-Space, as well as other universes, via the CVEs which they created. (TV: Logopolis, PROSE: Timewyrm: Apocalypse)
In 1981, the Tremas Master interfered with the Logopolitan project and inadvertently closed the CVEs. A wave of entropy then destroyed a large portion of the universe. On Logopolis, machines affected by entropy ceased to function and then crumbled. Parts of the Monitor, the Logopolitan leader, disappeared unevenly immediately prior to his actual disintegration. Whole stars and galaxies and many regions of the universe vanished, such as the Traken Union and Logopolis. The Logopolitans themselves were wiped out. The entropy was vented into E-Space. (TV: Logopolis)
The Black Guardian was the embodiment of entropy and chaos, opposed by the White Guardian, who embodied order. (TV: Enlightenment)
The Mandelbrot Set viewed Gabriel and Tanith as creatures that generated entropy and tried to kill them, only to be destroyed by them. (PROSE: Falls the Shadow)
A lifeform that evolved on Apollyon was a physical embodiment of entropy. (AUDIO: The Entropy Plague)
The final form of the Master was a sentient wave of entropy. In an aborted timeline, it was unleashed from Kiameth when the Saxon Master attempted to exploit the energy there to heal himself. The wave consumed Kiameth and then spread across all of N-Space, despite a parallel version of the Master putting the might of the Time Lords and Daleks against it. Eventually the wave returned to where it had began, the ruins of Kiameth. There it consumed Missy, causing a paradox which reset the universe. (AUDIO: Masterful)