Is there a way to replicate the Chrome Incognito Window using web technologies

I am wondering if there is a way to replicate the behavior of Chrome's private mode using we technologies. Let's say I want to run two web apps side by side in one tab of Chrome or any other browser but I want them to be isolated from each other so they do not share sessions for example. I am just wondering if there is anything that can get you close enough or even close to that.

A server can only read cookies that it sent to you. If the two web apps run in separate servers, they are isolated from each other. If they run on the same server, then you should have control over the code for the other web app and therefor should be able to make it just ignore cookies from the other app. You can't stop the computer itself from storing the website in its history and you can't really make it delete a cookie as soon as you leave the page (Well, you can, but that would defeat the purpose of a cookie). You could destroy the cookie/not "renew" it once the person logs off, but that's what the whole idea of "ending a session" is for...