# When to use quantum or classical statistical mechanics?

Jul 9, 2022

There are two main types of statistical mechanics: classical statistical mechanics and quantum statistical mechanics. Classical statistical mechanics is the branch of physics that studies the statistical properties of systems that are in thermal equilibrium, while quantum statistical mechanics is the branch of physics that studies the statistical properties of systems that are not in thermal equilibrium.

So, which one should you use?

The answer depends on the system you are studying. If the system is in thermal equilibrium, then you should use classical statistical mechanics. If the system is not in thermal equilibrium, then you should use quantum statistical mechanics.

Here are some more specific guidelines:

If the system is small and the interactions between the particles are weak, then you can use classical statistical mechanics.

If the system is large and the interactions between the particles are strong, then you should use quantum statistical mechanics.

If the system is in a highly excited state (i.e. it is not in thermal equilibrium), then you should use quantum statistical mechanics.

In general, if you are not sure which one to use, you should err on the side of using quantum statistical mechanics.

## Other related questions:

### Q: What is the difference between quantum and classical statistics?

A: Quantum statistics is the study of statistics of systems whose behavior is governed by the laws of quantum mechanics. Classical statistics is the study of statistics of systems whose behavior is governed by the laws of classical mechanics.

### Q: When should quantum mechanics be used?

A: Quantum mechanics should be used when studying systems that are very small, or when studying systems that are very cold.

### Q: Is statistical mechanics classical or quantum?

A: Statistical mechanics is a branch of physics that studies the behavior of systems composed of a large number of particles.

Classical statistical mechanics is the study of systems in which the particles are governed by classical mechanics, while quantum statistical mechanics is the study of systems in which the particles are governed by quantum mechanics.

### Q: Why do we proceed towards quantum mechanics rather than classical mechanics?

A: There are a few reasons why quantum mechanics is often favored over classical mechanics. First, quantum mechanics is generally more accurate than classical mechanics, particularly at very small scales. Second, quantum mechanics can describe phenomena that classical mechanics cannot, such as quantum entanglement. Finally, quantum mechanics is the basis for many modern technologies, such as lasers and transistors.