Statistical definition of entropy

By combining random flight statistics from Chap. 1 with the statistical definition of entropy from the last section, we shall be able to develop a molecular model for the stress-strain relationship in a cross-linked network. It turns out to be more convenient to work with the ratio of stretched to unstretched lengths L/Lq than with y itself. Note the relationship between these variables ... 

Planck Bed. Ber., 1908, 633) has, from the fundamental statistical definition of entropy, deduced the equation ... 

What is transported One of the peculiarities of the thermal energy variety is to think of the thermal conduction in terms of energy transported, when other domains consider entities as the transported quantity (charges, momenta, etc.). According to their definition, as entities bear energy, there is no physical consequence due to this disparity. There are naturally historical reasons for this, but also a conceptual difficulty in our modern minds to view the entropy as a quantity able to be transported. This is certainly due to the influence of the statistical definition of entropy as a measure of order/disorder in the system, considered as a whole with implicitly a uniform entropy distribution. 

Equation 8.1 is a statistical definition of entropy. Defining entropy in terms of probability provides a molecular interpretation of entropy changes as well as allowing for the cglpw iqj enfpja plangi fip qip H such as that of an ideal gas. In... 

This is exactly the same value that we obtained for this process in Example 8.1 using the statistical definition of entropy. 

The fact that this is an abaoltUe value arises from the statistical definition of entropy m equation (11 14). According to this equation the entropy would be zero if the system were known to be in a single quantum state. This point will be discussed in more detail in the next chapter in connexion with the third law. For the moment it may be noted that equation (12 64) leads to an apparent paradox—as T approaches zero it appears that 8 approaches an infinitely negative value, whereas the least value of 8 should be just zero, as occurs when the system is known to be in the single quantum state. This difiSculty is due to the fact that equation (12 8), on which the equations of the present section are based, becomes invalid at very low temperature. Under such conditions the Boltzmann statistics must be replaced by Einstein-Bose or Fermi-Dirac statistics. 

Since Ludwig Boltzmann (1844-1906) introduced a statistical definition of entropy in 1872, entropy is associated with disorder. The increase of entropy is then described as an increase of disorder, as the destruction of any coherence which may be present in the initial state. This has unfortunately led to the view that the consequences of the Second Law are self-evident or trivial. This is, however, not true even for equilibrium thermodynamics, which leads to highly nontrivial predictions. Anyway, equilibrium thermodynamics covers only a small fraction of our everyday experience. We now understand that we cannot describe Nature around us without an appeal to nonequilibrium situations. The biosphere is maintained in nonequihbrium through the flow of energy coming from the sun, and this flow is itself the result of the nonequilibrium situation of our present state in the universe. 

We, shall next consider the statistical definition of entropy in magnetic resonance. According to usual definition introduced by von Neumann, the quantum statistical definition of entropy is... 

---