Anonym said:
May you help me to understand what the temperature is?
Originally it introduced for the description of the statistical systems. Then one obtain U=1/2*k*T, namely, the relation not only for single particle but for the single degree of freedom of the single particle. Thus one obtain 1ev=11000deg. and therefore it correctly describes high energy physics. ?
From my understanding of the situation, temperature can be viewed several ways. In one case, from a termodynamic standpoint, you can define temperature as a constraint function of the configuration space when two systems are in thermodynamic equilibrium. Therefore, when two systems are in equilbrium, their temperature is the same.
The other way I've seen it come in is as a Lagrange multiplier for maximizing the entropy of a system at constant energy. You can define both quantities in terms of the density operator, and then maximize the entropy (by defining S = \hat{\rho} \ln \hat{\rho}) subject to the constraint that the energy expectation value is constant. When you do this, you recognize something that acts like the temperature, and therefore you call it "temperature".
I believe Pauli's "Treatise on Thermodynamics gives a more historic definition of temperature in terms of ideal gases, but this definition predates quantum mechanics, and is probably not the greatest way to go about thing.
Edit: As for the Shannon entropy thing, it is very easy to associate entropy with a lack of information about a system. In a state of zero entropy, as in full information, it would be possible for us to just build an enormous computer and numerically integrate the equations of motion from that point. The fact is, in a thermodynamic system we treat the system as a probabilistic one, since it is untractable to do what I just said. Shannon's entropy is very applicable to thermodynamics.
