Order of a system

It should be noted that studying states of order in thermal equilibrium as a function of temperature yields the possibility of measuring the degree of order of a system in values of corresponding equilibrium temperature . This way, the results of residual resistometry are independent of the detailed formalism between state of order and electrical resistivity... 

The first three editions of Beilstein are obsolete. The fourth edition (vierte Auflage) covers the literature from its beginnings through 1909. This edition, called das Hauptwerk, consists of 27 volumes. The compounds are arranged in order of a system too elaborate to discuss fully here. The compounds are divided into three divisions which are further subdivided into systems ... 

Entropy is a physical value that describes the degree of order of a system. The lower the degree of order, the larger the entropy. Thus, when a process leads to increase in disorder—and everyday experience shows that... 

C. A decrease in the order of a system corresponds to an increase in entropy. 

Intuitively, one might expect the order of a system to increase with decreasing temperature and that the minimum energy conformation of a molecule should be the one having the highest symmetry. In many cases, this is not the situation. 

This is equivalent to saying that the order formed in the nematic phase is not governed by electric dipole interactions but rather by the molecular shape and the van der Waals forces between molecules. Note that, although entropy is also related to the order of a system, the symbol S used here does not refer to entropy. 

Thus for a first-order uncontrolled process, the response of the closed-loop becomes second-order and consequently it may have drastically different dynamic characteristics. Furthermore, as we have seen in Sections 11.3 and 12.1, by increasing the order of a system, its response becomes more sluggish. Thus ... 

We can use frequency response techniques (see Chapter 17) to identify experimentally a poorly known process. Do you have any ideas on how you could do it To help you in your thoughts, consider the Bode diagrams of various systems that were examined in Chapter 17. Notice the information provided by characteristics such as the corner frequency (determines the unknown time constant), the level of low-frequency asymptotes (determines the value of static process gains), the slope of high-frequency asymptotes (determines the order of a system), and the behavior of phase lag (keeps increasing for systems with dead time). Note For further details, consult Ref. 11.)... 

It is well known that the entropy is a measure for the disorder of a system. It is clear that the entropy can serve also as a measure for the order of a system. However, the fact that we can understand entropy as a measure of symmetry is rather emphasized rarely. 

The AS " term is a measure of the increase or decrease in the order of a system. A more ordered system has less entropy and is less probable than a disordered one. The main factors that influence AS° in a chemical reaction are the number of moles of material on each side of the balanced equation and their physical state. The liquid phase of a substance has more entropy (less order) than the solid, and the gas phase has much more entropy than the liquid. Entropy increases when more molecules are formed at the expense of fewer ones, as for example in elimination reactions. Conversely, addition reactions convert more molecules to fewer ones and are characterized by a negative sign for AS ". 

Entropy chai (Section 3.9) The standard entropy change, A5°, is the change in entropy between two systems in their standard states. Entropy changes have to do with changes in the relative order of a system. The more random a system is, the greater is its entropy. When a system becomes more disorderly its entropy change is positive. 

This section gives the procedures that enable the output relative orders, the number and the orders of the zeros at infinity, and the essential orders of a system S to be determined directly from a bond graph representation. These procedures use the concepts defined in the previous sections. 

To predict the spontaneity of a chemical or physical process, we need to know the enthalpy change of the process and the change in entropy [W Section 13.2]. Entropy (S) often is described as a measure of the randomness or disorder of a system. The greater the disorder of a system, the greater its entropy. Conversely, the greater the order of a system, the smaller its entropy. 

Crystallization is the ordering of a disordered system. In order to follow this process, it is necessary to label atoms which have a crystalline local environment. This is done by quantifying the directional order of a system of bonds for each atom. Angular correlations at an atomic scale can be achieved by projecting interatomic vectors r, j onto a basis of spherical harmonics Yim (r ), and the order parameter of Steinhardt, Nelson, and Ronchetti has proved to be valuable in several contexts for different symmetries [32],... 

It is often interesting to change the order of a system to see how it affects the dynamics. This way, one gets more feel for what is important in the model, which eqiration really affects the dynamics. 

Figure 2.6. Bifurcation diagrams for the order parameter, which characterizes orientation ordering of a system at b=0,3>0 (bistability is observed in the temperature range Xi - T2), b=-0,3<0 (smooth transition between ordered and disordered states occurs in the temperature range Ti - T2), b = 0 (jump-Uke transition occurs between ordered and disordered states). The guiding parameter is a dimensionless temperature x=kT/El. Stable states are marked with solid lines, unstable states are marked with dashed lines.

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