It has been recently suggested in [1,2] that local interactions of the gravitational and/or Yang-Mills type can be responsible for a deterministic thermalization of the degrees of freedom of a finite dimensional system. Thus, the information paradox in a black hole is resolved: the process of formation and evaporation is entirely unitary and the apparent maximum-entropy state of the radiation from the black hole is produced by a deterministic, unitary process. For this to work, we need at the very least some examples in which the claimed properties hold. I will review the mathematical literature [4] which provides some examples of systems where the chaotic behavior is fully proven. These ideas have been used also in physics, particularly in classical Yang-Mills and the N-body gravitational problem [3]. As a bonus, these ideas can be used to produce deterministic random numbers [5] which are extensively used in Monte-Carlo simulations for HEP experiments (MIXMAX).
Reading list:
1] Shenker etal, 1512.00019,
2] Susskind etal, 1608.02612,
3] Gurzadyan & Savvidy, Collective Relaxation Of Stellar Systems, Astrophys.J. 160 (1986) 203-210
4] G. Savvidy, Anosov C-systems and random number generators, 1507.06348
5] K. Savvidy, The MIXMAX random number generator, Comput.Phys.Commun. 196 (2015) 161-165