Pseudo-temporal ordering in heterogeneous populations What's the most widely accepted tool for doing pseudo-temporal ordering from scRNAseq data? Also is there away to separate differential expression that occurs based on "cell identity" or maybe more accurately cell type fate from that which arises from cells being in different stages differentiation.

To be more concrete, lets say there's a population of cells, some of which were born at time 1, time 2, and time 3. The progression along the temporal trajectory can be described via a set of genes that are fluctuating as the cell matures. So you might have the same cell type which was born at time 1 be transcriptionally distinct from a younger one born at time 3.  On the other hand, within this population there are subpopulations which will have different cell fates and are transcriptionally distinct. Is there away to reliably separate the temporal axis from the "cell fate axes". If not is this something people are working on or is flawed logic to think this kind of thing is possible?
Regarding the first part of the question: scRNA-seq is a rapidly developing field so it may be hard to talk about "widely accepted tool for doing pseudo-temporal ordering from scRNAseq data". Few of the tools aiming to do just that include Monocole, Waterfall or Sincell (see this paper for references https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4122333/)

The second part is a bit more complex. Many aspects have come together here, e.g. cell-cycles, sub-populaitons identification and pseudo-temporal ordering, to get a true reflection of the biological processes. There are efforts on all (and more) these fronts (see again e.g. the above paper, though not the latest) and there are most likely people working on their integration. I'm not aware of any studies published yet at this depth though