How can you use the jQuery pjax plugin with Craft?
In order to make an AJAX call in Craft, you'll need to build a custom plugin. Within the context of your plugin, add a Controller as the end-point for your AJAX call. Once you've setup your controller, take a look at the EntriesService API methods to sort out exactly how to retrieve your entry data.

If you've never built a plugin or are unsure of where to begin, you can download this Business Logic template to use as a starting point. It comes pre-packaged with a controller containing a simple AJAX call (and a lot of "how-to" notes).

If you have any follow-up questions along the lines of "how do I collect the data for my AJAX call", those would be worthy of being their own Stack Exchange questions.