Do critics review first, second, and third novels differently? And if so, how?
What do critics think is the significance of the birth order of novels?
For me, a first novel is like an introduction, both for the author to the world of novels and to himself, and for the readership to the author.
Let's consider if the first novel is a complete clanger. Those who read it didn't like it, and not many did read it. It may be that the author thought they could write, wanted to test that theory, and with the complete failure of the book, decides not to pursue the hobby further. This isn't even a one-hit wonder, it's a one-hit miss.
Alternatively, the author takes on board comments received about why the book was rubbish, and pursues writing a second novel. In other words, the author views their first novel as a stepping stone, a learning process to move onto bigger and better things. This makes the first novel part of a bigger learning process.
However, when the first book is a success, this comes with its own set of problems; in some ways, you're in a more difficult spot than someone whose first book flopped.
For example, your book has been published in a particular genre, dealt with certain themes, had a particular style. These now have placed some boundaries on the author, particularly because it's likely you'll feel some pressure from the publisher to follow up on the success on the first.
Do you write something similar for your second? The publisher wants something as good, the readership you've gained may be expecting something similar. But how do you differentiate it enough to not be accused of simply copying your first work, yet still appeal to the same readership?
Do you stay in the same genre? Some genres are notoriously difficult to break out of e.g. science-fiction. If you have a readership that enjoyed your science-fiction novel, and suddenly your second book is a romance, your publisher may be at a loss to market you, and your readership will be terribly confused.
Therefore, for me, the first novel is an introduction to an author: their style, favoured genre, themes, etc. It's like meeting someone for the first time, and you get a general idea of what they're about. All I really expect this time is a good story well told.
What I expect from the second novel would be something similar, but different enough to show me that the author is versatile to not repeat past success be copying the same formula. I want to see progression from the author, too: depth, new characters, better detail, more writing skill. If you met someone for a second time, and they were completely and utterly different from the person you thought you knew, most of the time you'd be confused.
Unfortunately, many first time successful novelists spend a lot of time and effort on their first work, but when it's successful, they think they can duplicate that success by using a similar formula. This almost always fails in the sense that the writer hasn't grown, and it's likely that their audience won't, either.
So, I suppose you could say that the critical difference between the first and second, then, is one of expectation: from the readership, the publishers, even the author himself.
Beyond the second novel, I would say that the third is probably what cements your career: were the first two just flukes? Can you sustain it? Also, as you start writing more novels, you can sometimes become a bit freer in tackling other subjects, perhaps under a different name, like Ian Banks does when he writes science fiction as Ian M. Banks.