# Why this macro thing having quantum behaving but other not?

1. Feb 20, 2016

### fxdung

Why some macro phenomena have not quantum behaviour,but other phenomena have quantum behaviour?Why notions of temperature and heat are successfully in classical model and non-relativistic condition,despite they relate with energy and entropy that directly concern with quantum state ensemble?Whether do the notions of temperature and heat change when we consider effect of quantum and relativistic character of nature?What does control the self-cancelation quantum character in classical physics?

2. Feb 20, 2016

### A. Neumaier

This is a very long story usually treated in books on statistical mechanics.

Usually, the heavier the more classical. A quantum system with weight 1 gram is already very classical. Even if it is a superconductor. Though superconductivity is a quantum effect, but so is the fact that solids are hard. Treated in a phenomenological way, both facts can be handled in a completely classical way for engineering purposes.

3. Feb 20, 2016

### Demystifier

To behave quantum mechanically, the crucial requirement is to keep quantum coherence for a long time. For that purpose, the system is better to have a small number of active degrees of freedom. There are two ways how can that be achieved:
- By containing a small number of particles. (atom, few photons, ...)
- By containing a large number of particles in the same quantum state. (superfluid, superconductor, laser beam, ...)
In the latter case, it helps a lot if the temperature is low.

4. Feb 20, 2016

### fxdung

I hear that there is Thermal Quantum Field Theory,then what are the notions of temperature and heat in QFT and QM?Is that it bases on entropy so then on statistic quantum state ensemble or the classical notions of temperature and heat(basing on classical chaos motion of classical particles) still be able to use in QM and QFT?Does the book of QFT of Zinn-Justin say about this topic?

5. Feb 21, 2016

### A. Neumaier

Quantum statistical mechanics uses entropy and temperature in analogy to (but not equivalent with) classical mechanics.
I recommend the book on statisitcal physics by Linda Reichl. On a more advanced level the book by Calzetta and Hu on nonequilibrium QFT.

6. Feb 22, 2016

### fxdung

Then I think Thermodynamics is classically,universally describle theory of aggregate matter,so that we can use intact classical notion of temperature in Quantum Mechanics.E.g the Bose-Einstein and Fermi -Dirac quantum statistic distributions use classical temperature in their formula.And in Quantum Field (e.g electromagnetic radiation) Theory we use quantum entropy to construct the notion of temperature.Is that right?

7. Feb 22, 2016

### A. Neumaier

There is no difference between classical temperature and quantum temperature, since upon quantization, temperature (just like time) does not become an operator.

In each case, the quantum version is obtained from the classical version by replacing the classical extensive quantities by their operator version and the phase space integral by a trace. See Chapter 8 of my online book.

8. Feb 22, 2016

### fxdung

Why are only extensive quantities to be replaced by operators but not for other quantities e.g intensive quantities?

9. Feb 22, 2016

### A. Neumaier

Because intensive quantities are just parameters in the description of the state.
This is immediate for parameters such as temperatures, which directly go into the expression for the density matrix (in a canoncal ensemble, say).

But it holds generally. For example, to go from an extensive quantity to the corresponding normalized intensive quantity one needs to divide by the mean mass or a similar expectation, and hence depends on the state.

10. Feb 22, 2016

### A. Neumaier

Time is a coordinate and not a thermodynamic quantity. But it is intensive, as having 1000 objects at time $t$ doesn't multiply the time by 1000.

11. Feb 22, 2016

### fxdung

So,the state depend on time.Then time is a parameter.