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spaghetti3451

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- Thread starter spaghetti3451
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In summary, classical physics can only deal with discrete states, whereas quantum mechanics allows for states that are not discrete.

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spaghetti3451

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chrisbaird

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But more to your question, strictly speaking this is misleading. You should instead speak about the density of occupied particle states in

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Bill_K

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Why are we doing this then?

Because it's a heckuva lot easier to deal with discrete states, and take the continuum limit at the end.

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chrisbaird

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First of all, in classical physics, we don't have a natural unit for the phase-space volume. In quantum theory we know it's given by [itex]h^{6N}=(2 \pi \hbar)^{6N}[/itex]. Thus, one can divide the phase-space volume in hypercubes with this volume and do statistics by "counting".

Second, you must apply the notion of indistinguishability of particles to avoid the Gibb's paradox.

Third, the entropy is bounded from below if there's a gap between the ground state (vacuum/quasi-particle vacuum) and the lowest excited state, from which follows Nernst's theorem of heat (the third Law of thermodynamics).

I guess there are a lot more examples, where you need a minimal version of quantum mechanics when doing classical physics. Thus, it's much better to learn statistical physics after having heard a bit about quantum theory before and consider the (quasi-)classical limit of quantum statistics to derive classical statistics.

This is also an important fundamental step: It explains, how a classical world appears for macroscopic objects although the underlying principles of our world is quantum on the fundamental level.

Quantum ideas are used in classical statistical physics as a way to describe the collective behavior of large numbers of particles. This approach, known as quantum statistical mechanics, uses the principles of quantum mechanics to explain the macroscopic behavior of systems at the microscopic level.

One example is the use of the density matrix, which is a quantum concept, to describe the statistical properties of a classical system. Another example is the use of the partition function, which is derived from quantum mechanics, to calculate thermodynamic quantities such as free energy and entropy.

Quantum ideas provide a more accurate and comprehensive understanding of classical systems by taking into account the underlying quantum nature of matter. This allows for a more precise description of complex systems and can lead to new insights and predictions.

One challenge is the mathematical complexity of quantum mechanics, which can make it difficult to apply to classical systems. Another challenge is the need for specialized techniques and approximations to deal with the quantum effects in classical systems.

The use of quantum ideas in classical statistical physics has many potential applications, including the study of phase transitions, the behavior of materials at extreme conditions, and the development of new materials and technologies. It also has implications for fields such as condensed matter physics, biophysics, and cosmology.

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