Is remarriage perpetual adultery?

I'm inclined to believe it isn't, but this is something I've heard from some Christian folks. Some go as far to say every time you have sex with anyone who isn't your first spouse, you're committing adultery and that remarriage is not a real marriage but is simply "an adulterous relationship."

What are your thoughts? Do you agree with this? And if someone is remarried after an unbiblical divorce, what does repentance look like?