Probability state

From standpoint of aims of the technical diagnostics (TD) it is necessary to select two probable states of the NDT objects (NDTO). The first, when defect in the material already has been formed might characterize as defective state of material (DSM). And second - when defect is not yet formed, but exist so changes in the spatial (volume) distribution (SD) of the physical-mechanical features (PMF) of the material, of its tense-deformed state (TDS), which under certain conditions will initiate defect origination. This is predefective state of material (PDSM). 

Systems tend to proceed from ordered low entropy or low probability) states to disordered high entropy or high probability) states. 

The path variables of the PPM corresponds to the cluster probabilities of the CVM by which the free energy is minimized to obtain the most probable state. Likewise, under a set of constraints, the PPF is maximized with respect to the path variables for each time step, which yields the optimized set of path variables. Since a set of path variables, + At), relates cluster probabilities t and at time t + At... 

Figures 3.24 and 3.25, for example, show the probabilities for the 2 ° pos.sible configurations on an = 10 lattice obtained at time t = 10 for evolutions by rules R126 and R30 (both in class c3), respectively. The figures show that the evolution modifies the probabilities of states from initially being equally likely to distributions in which individual configurations can have widely differing final probabilities. The properties of the more probable states will then tend to dominate the statistical averages over the enseiiible.

Keywords fluxon gas in thermalized Josefson systems the criteria of degeneracy of the relativistic ideal gas absolute minimum realization of the most probable state in the equilibrium system temperature of the primary microwave cosmic background primary quantum magnetic flow. 

In order to define the statistical characteristics of a many particle system, for instance an ideal gas, their distribution function with some defined physical parameters (for example, velocity, momentum, energy, etc) should be fully determined. In particular it is physically important to define the velocity of particles corresponding to the most probable state, which is the maximum of the distribution function. 

Analysis of the last formula shows that in both cases, in principle, we can observe the minimal intensity of radiation or magnetic flow. This is in agreement with the absolute minimal realization of the most probable state in equilibrium system (see fig 3.a and fig 4.a, fig 3.b and fig 4.b). They are in agreement with the values of the observed distribution function observable frequencies and are equal to Im = f(xm) for fluxons and lm = f(xm) for radiating particles. For details of statistical characteristics of observable frequencies see reference (Jumaev, 2004). 

As follows from the previous analysis for quasi and ordinary particles gases there exists a critical value of parameters a and b for which the least value of the distribution function for observable frequencies is observed. From the physical point of view this is in agreement with the absolute minimal realization of the most probable state. As in any equilibrium distribution, there is an unique most probable state which the system tends to achieve. In consequence we conclude that the observable temperature of the relic radiation corresponds to this state. Or, what is the same, the temperature of such radiation correspond to the temperature originated in the primary microwave cosmic background and the primitive quantum magnetic flow. 

Figure 1. (la) Distribution function of the velocity for the relativistic ideal gas of gluxions. (2a) Distribution functions of the observable frequencies. (3a) Most probable values of the observable frequencies as function of a. (4a) Absolute minimal realization of most probable states of system. 

As mentioned above, results from kinetic experiments [53, 54, 62] are inconclusive about the state of activated cisplatin, and have under some experimental conditions (chloride-depleted environment) revealed the most probable state of activated cisplatin to be the mono-aquated form, cis-Pt[Cl][NH3]2[H20]+. The first aquation reaction has been determined to be approximately two orders of magnitude faster than the second. This opinion is far from undisputed, however, and results from other experiments, based on the ratio of the amounts of DNA adducts formed by the different aquated cisplatin moieties [54], strongly indicates that the likely state of cisplatin binding to DNA is in fact the diaquated state. 

In an open system, the most probable state [P= cexp( /kT)] is the one with the smallest value for the free energy F= U— TS. 

Figure 3.6 shows the various relationships between the energy levels of solids and liquids. In electrolytes three energy levels exist, Ep, redox, Eox and Ered- The energy levels of a redox couple in an electrolyte is controlled by the ionization energy of the reduced species Ered, and the electron affinity of the oxidized species Eox in solution in their most probable state of solvation due to varying interaction with the surrounding electrolyte, a considerable... 

Still another consideration is that this point of view, especially where at least one of the molecules is large and complex, lends itself readily to thinking in terms of more than one reaction path. That is, it is more apparent that there can be various similar configurations whose overall contribution to the rate may be similar, and hence competitive. Some may have a high activation energy but represent a very probable state of affairs others may have a low activation energy but an improbable state of affairs. In other words, many related reaction paths can be present. 

The numbers succeeding the asterisk show that equilibrium was in all probability then attained. The dotted curve, Fig. 8, shows the probable state which would occur if the reactions balanced as in the ideal state indicated in Fig. 7. Indeed, if the temp, exceeds 490°, the final state is the same whatever be the initial products. The space between the two lines represents a system below 490° in what P. Duhem calls un etat de faux equilibre. The region where there is no reaction and where... 

The concepts of equilibrium as the most probable state of a very large system, the size of fluctuations about that most probable state, and entropy (randomness) as a driving force in chemical reactions, are very useful and not that difficult. We develop the Boltzmann distribution and use this concept in a variety of applications. 

When the probability of occurrence, P, described above appears to be the objective probability (stated probability), the degree of anxiety that is standardized by using its maximum value, AEi>=1, can be regarded as the subjective probability. From this consideration, it is possible to explain the above new degree of anxiety as follows. There is a two-stage process in which people first assess the objective probability of an uncertain event and then transform this value by a subjective probability that is in proportion to the degree of anxiety. The relationship between the difference of the two probabilities and objective probability is shown in Figure 6.4. 

In an irreversible process, in conformity with the second law of thermodynamics, the magnitude that determines the time dependence of an isolated thermodynamic system is the entropy, S [23-26], Consequently, in a closed system, processes that merely lead to an increase in entropy are feasible. The necessary and sufficient condition for a stable state, in an isolated system, is that the entropy has attained its maximum value [26], Therefore, the most probable state is that in which the entropy is maximum. 

Moreover, fluctuations represent one of the most fundamental concepts of statistical mechanics and/or thermodynamics (not included in traditional thermodynamics). When the atom number is large enough (at least some hundred of atoms), the properties of the systems can be calculated in the most probable state. As quoted in Section 3 of the present chapter, the... 

An actual proof of statement II or its derivation from statement I does not exist. It would serve as a basis for the study of deviations from the most probable state (cf. Section 25). In this sense the papers quoted there give the most thorough discussion of this question. 

Thermodynamics provides us with tools to determine the equilibrium state, i.e., the most probable state that exists under specified conditions such as temperature, pressure, and composition. The happy message provided by classical thermodynamics is that the most probable state is that which has... 

Probable states of aggregation that have not been structurally authenticated are in parentheses. 

Macroscopic systems are composed of large numbers of interacting particles, and the state variables represent either averages of instantaneous states over a long time interval, or the most probable states. Most systems communicate with the environment by exchanging small quantities of matter, momentum, or energy, which are treated as experimental error and, confidence level. So, the instantaneous state of a system is not stationary state Xs but rather nearby state X related to Xs through the perturbation x(t) X(t) =Xs + x(t). 

We have seen that processes are spontaneous when they result in an increase in disorder. Nature always moves toward the most probable state available to it. We can state this principle in terms of entropy In any spontaneous process there is always an increase in the entropy of the universe. This is the second law of thermodynamics. Contrast this law with the first law of thermodynamics, which tells us that the energy of the universe is constant. Energy is conserved in the universe, but entropy is not. In fact, the second law can be paraphrased as follows The entropy of the universe is increasing. 

Gas molecules tend to their most likely distribution in space. Tlie molecules of an ideal elastomer tend to their most probable conformation, which is that of a random coil. The most probable state in either case is that in which the entropy is a maximum. 

Steps (45), (46), and (48) can be eliminated since they would be strongly endothermic with ground-state SO, which would be the most probable state when sulfur atom source is the photolysis of CSj. Thus to account for S2O formation in the CS2-O2 system, only steps (47) and (49) seem reasonable at room temperature. 

---