How does the realist theory of international relations in the article "structural realism" by John Mearsheimer answer the question of what causes war between two states? According to these answers, what factors will determine whether war occurs between the United States and China in the 21st century?

In John Mearsheimer's paper, "Structural Realism," he explains that a war among or between great powers can be explained by a number of reasons, depending on the school of political theory to which one ascribes. Security is one such reason. One principle difference is whether a condition of bipolarity (two great powers) or multipolarity (several great powers) is operative. Those arguing that bipolarity is more peaceful point to the World Wars in the multipolar early twentieth century, and those arguing that bipolarity is more peaceful point to the peace of the early nineteenth century compared to the Cold War.
A number of additional, non-empirical factors, contribute to the relative stabilities of bipolarity and multipolarity. In bipolar circumstances, power is more balanced; however, in multipolar conditions, there is less targeted hostility.
Others still point to the "preponderance theory," which maintains that the most peaceful conditions exist when one power feels secure in its leading position (proponents of this point to the post-Napoleonic wars). Critics of this theory claim that the nature (or "dynamics") of this preponderance need to be investigated before peace can be assured.
As to whether China can rise peacefully, Mearsheimer is rather ambiguous. That said, it is suggested by offensive realists that, insofar as the United States is now a hegemon (and so represents a "preponderant" power), it is reasonable that the United States might engage in a defensive war. According to defensive realists, however, there will be little security competition between the US and a rising China, because of the existence of nuclear power, and because China's dominance of Asia poses little practical threat to US interests.