Negotiations broke down and war was declared.
War broke out between the two countries.
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Sign up to join this community"War" has several noun definitions, including:
Both your examples refer to declarations of war which are a state or situation, which is why they do not require an article.
Consider as an example:
"Swimming" is here used as a noun for the act of swimming. There is no need for an article.
"Swim" is also a noun here, but because it refers to a specific swim, an article is used.
Likewise: