Actually this exact question was asked more than 2 years ago. The common theme there is about the same answer I offer below, but it’s worth a look.
But it’s funny, at first instance you think “oh yeah…of course”…and then try to actually name a book like what you’re asking for and it turns out to be a lot tougher than you realize. I would have thought I could rattle off at least a few good sources for what you’re after. But I think the reason it’s a little more difficult is because the real answer is in all the abundance you see around you. Anywhere you see prosperity it’s the result of (at least some degree of) free enterprise and free trade. I think it may be much easier to empirically prove how any other system hinders this progress.
In addition, as mentioned in that thread I think the general concept of freedom cannot be ignored. As Friedman said “capitalism is not a sufficient condition for freedom. It’s a necessary condition.” It’s not that you have freedom wherever you have capitalism, but you have capitalism wherever you have freedom. And I think that actually may be a more important way to approach it…the fact that wherever people are free to choose, they engage in free commerce…and when they are subjected to much more restrictive conditions, they try to go elsewhere. I think the simple instances of Hong Kong vs. China (mentioned by Friedman in that link) and West Germany vs. East Germany…the fact of how people voted with their feet…is some of the best empirical evidence for the superiority of capitalism and free trade you’ll ever get.
However, as I was saying, I think it may be the easier case to show how any intervention with a free market only hinders economic growth and progress, and virutally always ends up doing more harm than good. (This is the importance of Hazlitt’s one lesson. Any time you try to make that case your opponents will hand pick an individual isolated example of a single person or group who benefited from some government action, but of course they ignore the costs and unintended consequences. It is these who are the truly “forgotten men”, and it is this sort of evidence that virtually any free-market oriented text will offer at least some degree of.
But for the positive kind you’re after, the first thing that comes to mind is actually Matt Ridley’s concept of “when ideas have sex”. The guy is almost a total academic, with several degrees in zoology actually…so he comes from a hard science field that is hard to simply dismiss as biased or “partisan”…Plus he has a really intelligent-sounding British accent, so that should win over most people right there. But throughout this speech he offers multiple empirical factors that point to free enterprise and free trade as the source for prosperity. He shows how when people are able to trade freely, technology and quality of life improves, and when that trading ability is taken away or cut off, not only does growth decline and even cease, but it can actually regress.
I’ll add more as I think of them, but others you might look into would be:
Basic Economics and Economic Facts and Fallacies by Thomas Sowell. (Actually a great deal of his economics books offer quite a bit of history and empirical evidence)