The question of whether all non-quantum physical systems can be efficiently simulated on a classical computer is still an open problem in physics and computer science. This question is closely related to the concept of computational complexity and the class of problems known as "P" (problems that can be solved efficiently) versus "NP" (problems that can be verified efficiently).
Currently, there is no proof that shows that all non-quantum physical systems can be efficiently simulated on classical computers. In fact, there are many complex physical systems for which simulating their behavior is computationally challenging, even for powerful classical computers. Examples include systems with a large number of interacting particles, such as complex fluids or strongly correlated materials, where simulating their behavior accurately can be extremely demanding.
However, it's important to note that the concept of "efficiently simulated" depends on the specific problem and the computational resources available. While some physical systems might be difficult to simulate accurately, approximations and computational techniques can often be employed to gain useful insights.
The advent of quantum computers, on the other hand, has the potential to provide a significant boost in computational power, enabling more efficient simulation of certain quantum systems. Quantum simulators and quantum algorithms specifically designed for simulating quantum systems hold promise in this regard.
In summary, while it is currently unknown whether all non-quantum physical systems can be efficiently simulated on classical computers, it is an area of ongoing research and a topic of great interest in both physics and computer science.