There is no obligation to maintain the secrecy of information simply because it would likely be classified Top Secret. In the absence of a secret designation, legally generated information is free to disseminate.
Under "Born Secret" doctrine, the answer is different. In those cases, the government does not designate information as classified; the information is classified without any action being taken by the government. But it's too narrow to be applied to just any information that could be classified. As originally enacted (the statute has been moved to somewhere else in the U.S. Code, and I can't find it), the Atomic Energy Act of 1946's Born Secret provisions only apply to disclosures of:
- "data concerning the manufacture or utilization of atomic weapons, the production of fissionable material, or the use of fissionable material in the production of power";
- made "with intent to injure the United States or with intent to secure an advantage to any foreign nation" or with knowledge that another will use the information with such an intent.
So if an inventor revealed the existence of the atomic weapon she invented, but not data concerning its manufacture, that shouldn't implicate Born Secret. Or if the inventor revealed data concerning the manufacture of the invention, but did reasonably believed that the data would not be used to injure the United States or secure an advantage with a foreign nation, that should also be permissible.
Beyond Born Secret, there's also the Invention Secrecy Act, but my understanding is that it only applies to inventions for which the inventor has applied for a patent.
Of course, all of this assumes that Born Secret or the Invention Secrecy Act can withstand a First Amendment analysis, which is hardly certain. Under Bartnicki v. Vopper, 532 U.S. 514, 527 (2001) "state action to punish the publication of truthful information seldom can satisfy constitutional standards." There's obviously a strong argument to be made that an atomic bomb how-to would be a good exception. This was the subject of United States v. Progressive, which was never resolved.
Both restrictions also implicate the Fifth Amendment's Takings Clause, though the Invention Secrecy Act makes some provisions for compensation to the inventor.