By Professor Daijiro Yoshioka (auth.)
This e-book presents a accomplished presentation of the fundamentals of statistical physics. the 1st half explains the essence of statistical physics and the way it presents a bridge among microscopic and macroscopic phenomena, permitting one to derive amounts akin to entropy. the following the writer avoids going into info resembling Liouville’s theorem or the ergodic theorem, that are tough for newcomers and pointless for the particular software of the statistical mechanics. within the moment half, statistical mechanics is utilized to varied platforms which, even supposing they give the impression of being various, proportion an analogous mathematical constitution. during this means readers can deepen their realizing of statistical physics. The e-book additionally good points purposes to quantum dynamics, thermodynamics, the Ising version and the statistical dynamics of unfastened spins.
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Additional info for Statistical Physics: An Introduction
Sample text
4 Pressure of an Ideal Gas: Quantum Mechanical Treatment In Chap. 1, we derived the pressure of an ideal gas as P = 2E/3V using classical mechanics. However, molecules are governed by quantum mechanics, not by classical mechanics. The use of quantum mechanics to describe the state of a molecule is essential for statistical physics. Therefore, we need to calculate the pressure quantum mechanically, and verify that we obtain the same result. The pressure obtained quantum mechanically is compared with the pressure obtained from the entropy in the next section.
At the microscopic level, the motion is governed by quantum mechanics. As we shall see in Chap. 4, the motion of molecules is quantized, and we can count the number of microscopic states even for a gas molecule in a container. As a consequence of quantum mechanics, the energy is quantized also. That is, the kinetic energy of a molecule is no longer a continuous variable. This fact gives us an answer to question 3. Namely, we need a nonzero δE to have a reasonable behavior of W . If we make δE arbitrary small, W ceases to be a well-behaved function of E.
Another example is a conductor connected to a battery. In this case an electric current flows in the conductor. The systems in these examples are in quasi-stationary nonequilibrium states. That is, energy is continuously put into the system, and the nonequilibrium state lasts for a long time. On the other hand, there are also situations where a nonequilibrium state is prepared by some means or other, and after that the system is left to evolve by itself without further input of energy from outside.