# Low-entropy problem

##### Image: The part of phase space, with total volume corresponding to an end-point of the universe in which all matter has been absorbed into black holes, corresponding to the initial state of the universe, must be chosen with a precision equal to one part in 10 to the power 10^{123}.

Links

Scholarpedia: Time’s arrow and Boltzmann’s entropy >

Wikipedia: Loschmidt’s paradox >

### Multimedia

Talks by David Wallace and Roger Penrose in ‘The Arrow of Time’ miniseries