Let me say that, although the question could easily introduce opinion-based answers. To avoid this danger, I'll try to stick to our present knowledge and understanding, avoiding any speculation on the future evolution of the field.

I think that two related assumptions are underlying this question and should be elicited.

The first is that computation always implies the possibility of predicting the behavior of a system. I think that this assumption strongly overlooks what computation is. The physical basis of any simulation is to establish a mapping between the steps of an algorithm and the states of a time-evolving physical system (the computer). Therefore, to have predictions, we need an algorithm sufficiently powerful and a physical system with enough states to describe the system of interest. The typical approach is to find a suitable set of basic building blocks such that a faithful algorithmic description of their behavior is possible. For example, we can start with atoms, interaction laws, and a few prescriptions for their dynamic behavior. Then, we map a starting configuration of atoms into some internal state (bits, qubits, or whatever we can use) of a physical system (the computer), and we start its dynamical evolution mirroring the steps of the algorithm.

It should be clear that his kind of computation is just a way to have the full information on the microscopic states of the system in the cases it is not possible to obtain the same information by direct measurements on the system of interest. The best prediction we may hope to get from this kind of computation is predicting the final microscopic state after some time. Now, the real question is if this kind of prediction is really what we are looking for. I think that the factual answer coming from the present status of Science is negative. The bare detailed knowledge of the microscopic state may be an interesting result but does not provide insight by itself. This observation brings us to the second assumption.

The second implicit assumption of the question is that Statistical Physics exists only because of our limited computational capabilities. I think the history of Statistical Physics shows that it is a theory designed to extract the emergent phenomena in complex systems. Therefore, it should not be seen as expedient to overcome limited computational abilities but as the scientific way to get insight from a microscopic description by a systematic and controlled coarse-graining process.

For the above reasons, my answer to the question in the title is the following.

Our present limited computational capacity seems to preclude the possibility of direct modeling of arbitrarily complex systems. However, at least for those systems about which we do not need the full information about the initial state, we could model them better and better. Then, a good understanding of the meaning of computation would suggest that there is nothing in the present state of things hampering an asymptotic faithful representation of their behavior. However, the possibility of a faithful mapping of a complex system into another system of the same complexity is completely useless for the advancement of our knowledge. In this sense, present or future limits of computation do not look like a fundamental obstacle. The real limit is in our capacity of making sense of the results. It is a fact that Statistical Physics has been developed mainly for that purpose. If in the future, this branch of Physics or some evolution of it could help, it can only be matter of opinion.

The question could easily introduce opinion-based answers. To avoid this danger, I'll try to stick to our present knowledge and understanding, avoiding any speculation on the future evolution of the field.

I think that two related assumptions are underlying this question and should be elicited.

The first is that computation always implies the possibility of predicting the behavior of a system. I think that this assumption strongly overlooks what computation is. The physical basis of any simulation is to establish a mapping between the steps of an algorithm and the states of a time-evolving physical system (the computer). Therefore, to have predictions, we need an algorithm sufficiently powerful and a physical system with enough states to describe the system of interest. The typical approach is to find a suitable set of basic building blocks such that a faithful algorithmic description of their behavior is possible. For example, we can start with atoms, interaction laws, and a few prescriptions for their dynamic behavior. Then, we map a starting configuration of atoms into some internal state (bits, qubits, or whatever we can use) of a physical system (the computer), and we start its dynamical evolution mirroring the steps of the algorithm.

It should be clear that his kind of computation is just a way to have the full information on the microscopic states of the system in the cases it is not possible to obtain the same information by direct measurements on the system of interest. The best prediction we may hope to get from this computation is predicting the final microscopic state after some time. Now, the real question is if this kind of prediction is really what we are looking for. I think that the factual answer coming from the present status of Science is negative. The bare detailed knowledge of the microscopic state may be an interesting result but does not provide insight by itself. This observation brings us to the next point.

The second implicit assumption of the question is that Statistical Physics exists only because of our limited computational capabilities. I think the history of Statistical Physics shows that it is a theory designed to extract the emergent phenomena in complex systems. Therefore, it should not be seen as expedient to overcome limited computational abilities but as the scientific way to get insight from a microscopic description by a systematic and controlled coarse-graining process.

For the above reasons, my answer to the question in the title is the following.

Our present limited computational capacity seems to preclude the possibility of direct modeling of arbitrarily complex systems. However, at least for those systems about which we do not need the full information about the initial state, we could model them better and better. Then, a good understanding of the meaning of computation would suggest that there is nothing in the present state of things hampering an asymptotic faithful representation of their behavior. However, the possibility of a faithful mapping of a complex system into another system of the same complexity is completely useless for the advancement of our knowledge. In this sense, present or future limits of computation do not look like a fundamental obstacle. The real limit is in our capacity of making sense of the results. It is a fact that Statistical Physics has been developed mainly for that purpose. If in the future, this branch of Physics or some evolution of it could help, it can only be matter of opinion.

Let me say that, although the question could easily introduce opinion-based answers. To avoid this danger, I'll try to stick to our present knowledge and understanding, avoiding any speculation on the future evolution of the field.

I think that two related assumptions are underlying this question and should be elicited.

The first is that computation always implies the possibility of predicting the behavior of a system. I think that this assumption strongly overlooks what computation is. The physical basis of any simulation is to establish a mapping between the steps of an algorithm and the states of a time-evolving physical system (the computer). Therefore, to have predictions, we need an algorithm sufficiently powerful and a physical system with enough states to describe the system of interest. The typical approach is to find a suitable set of basic building blocks such that a faithful algorithmic description of their behavior is possible. For example, we can start with atoms, interaction laws, and a few prescriptions for their dynamic behavior. Then, we map a starting configuration of atoms into some internal state (bits, qubits, or whatever we can use) of a physical system (the computer), and we start its dynamical evolution mirroring the steps of the algorithm.

It should be clear that his kind of computation is just a way to have the full information on the microscopic states of the system in the cases it is not possible to obtain the same information by direct measurements on the system of interest. The best prediction we may hope to get from this kind of computation is predicting the final microscopic state after some time. Now, the real question is if this kind of prediction is really what we are looking for. I think that the factual answer coming from the present status of Science is negative. The bare detailed knowledge of the microscopic state may be an interesting result but does not provide insight by itself. This observation brings us to the second assumption.

The second implicit assumption of the question is that Statistical Physics exists only because of our limited computational capabilities. I think the history of Statistical Physics shows that it is a theory designed to extract the emergent phenomena in complex systems. Therefore, it should not be seen as expedient to overcome limited computational abilities but as the scientific way to get insight from a microscopic description by a systematic and controlled coarse-graining process.

For the above reasons, my answer to the question in the title is that our limited computational capacity is not a fundamental obstacle.

Let me say that, although the question could easily introduce opinion-based answers. To avoid this danger, I'll try to stick to our present knowledge and understanding, avoiding any speculation on the future evolution of the field.

I think that two related assumptions are underlying this question and should be elicited.

The first is that computation always implies the possibility of predicting the behavior of a system. I think that this assumption strongly overlooks what computation is. The physical basis of any simulation is to establish a mapping between the steps of an algorithm and the states of a time-evolving physical system (the computer). Therefore, to have predictions, we need an algorithm sufficiently powerful and a physical system with enough states to describe the system of interest. The typical approach is to find a suitable set of basic building blocks such that a faithful algorithmic description of their behavior is possible. For example, we can start with atoms, interaction laws, and a few prescriptions for their dynamic behavior. Then, we map a starting configuration of atoms into some internal state (bits, qubits, or whatever we can use) of a physical system (the computer), and we start its dynamical evolution mirroring the steps of the algorithm.

It should be clear that his kind of computation is just a way to have the full information on the microscopic states of the system in the cases it is not possible to obtain the same information by direct measurements on the system of interest. The best prediction we may hope to get from this kind of computation is predicting the final microscopic state after some time. Now, the real question is if this kind of prediction is really what we are looking for. I think that the factual answer coming from the present status of Science is negative. The bare detailed knowledge of the microscopic state may be an interesting result but does not provide insight by itself. This observation brings us to the second assumption.

The second implicit assumption of the question is that Statistical Physics exists only because of our limited computational capabilities. I think the history of Statistical Physics shows that it is a theory designed to extract the emergent phenomena in complex systems. Therefore, it should not be seen as expedient to overcome limited computational abilities but as the scientific way to get insight from a microscopic description by a systematic and controlled coarse-graining process.

For the above reasons, my answer to the question in the title is the following.

Our present limited computational capacity seems to preclude the possibility of direct modeling of arbitrarily complex systems. However, at least for those systems about which we do not need the full information about the initial state, we could model them better and better. Then, a good understanding of the meaning of computation would suggest that there is nothing in the present state of things hampering an asymptotic faithful representation of their behavior. However, the possibility of a faithful mapping of a complex system into another system of the same complexity is completely useless for the advancement of our knowledge. In this sense, present or future limits of computation do not look like a fundamental obstacle. The real limit is in our capacity of making sense of the results. It is a fact that Statistical Physics has been developed mainly for that purpose. If in the future, this branch of Physics or some evolution of it could help, it can only be matter of opinion.