Entropy is antithetical to immortality

The quest for immortality spans all of human history, from as early as the epic of Gilgamesh (circa 5000 B.C) to modern biotechnology and brain simulation and uploading.

There's only one problem - Entropy.

The second law of thermodynamics states how systems inevitably move towards disorder and break down eventually. So will all of our attempts towards immortality, whether physical or digital, as long as they obey our physical laws of existence, cannot succeed indefinitely.

Greg Egan's book “Permutation City” discusses a protagonist and his attempt at creating a universe that expands indefinitely, in which current physical laws are avoided: the TVC universe. the TVC universe is based on N-dimensional cellular automata, which expands by duplicating itself while avoiding entropy. 

My question therefore is - how can such a universe (that allows for actual immortality) exist? 

I believe that we (anyone interested in “true immortality”) has to start working in this direction.

-G