Entropy spin system

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

Notice that dephasing of the transverse magnetization does not affect Mz a T2 process involves no energy transfer but, being a spontaneous process, does involve an increase in the entropy of the spin system. 

As is apparent from Figure 10.1, an a-helical structure imposes fairly rigid constraints on the relative positions of successive residues in a peptide chain. Thus there is a loss of entropy that must be overcome energetically in order for an a-helix to form. To explain the underlying biophysics of this system, John Schellman introduced a theory of helix-coil transitions that is motivated by the Ising model for one-dimensional spin system in physics [180, 170],... 

FIGURE 11 An entropy function in the sense of fluctuation (i.e., large-deviation) theory, describing how fast the mean magnetization of a spin system gets classical with an increasing number of spins. The figure is based on an approximate calculation for the Curie-Weiss model. The temperature is fixed and has been taken here as one third of the critical (Curie) temperature. Above the Curie temperature the respective entropy Sn ,an would only have one minimum, nameiy, at m = 0. 

The term spin diffusion has been coined by Bloembergen [1] to characterize the polarization-exchange process in a strongly dipolar-coupled many-spin system. As pointed out by Bloembergen, this process leads to a spatial spread of polarization originating on a given spin that mimics, under certain conditions, a diffusion process. In a true diffusion process, the entropy increases monotonically. In the exact quantum description of the spin-diffusion process, however, the entropy is conserved and the process is, in principle, fully reversible. 

Two methods are described here the hypothetical scanning method and the local states (LS) method. Both were developed originally for spin systems and are discussed in a later section, but for simplicity we illustrate how they have been applied to a model of SAWs on a square lattice. These methods enable one to extract the approximate entropy from a sample simulated by any technique, in particular by the MC or the MD procedures. They are based on the concept that two samples in equilibrium generated by different simulation methods are equivalent in the sense that they lead to the same estimates (within statistical error) of average properties, such as the entropy, energy, and their fluctuations. ... 

Considering a generalized spin system, with no applied pressure, nor the lattice entropy contribution, the implicit dependence of tr on temperature is... 

The values of S° represent the virtual or thermal entropy of the substance in the standard state at 298.15 K (25°C), omitting contributions from nuclear spins. Isotope mixing effects are also excluded except in the case of the H—system. 

A certain ambiguity arises in the proper choice of the thermodynamic parameter p, since entropy changes due to solvent orientation are neglected. The available experimental data (cf. Sect. 4) indicate, however, that the free energy of reaction for systems showing a spin change is close to zero. The numerical analysis has been therefore performed for the specific case p = 0, for which value the rate constant in Fig. 15 has been computed as a function of S and h lkgT. 

A to B, while a temperature drop, ATad, is observed during the adiabatic process A C. The maximum magnetic entropy for a system with a spin s, ftln(2s+ 1), reached at infinite temperatures, is indicated as a grey broken line. 

Figure 9.1 Spin angular momenta, s, depicted as arrows, are randomly aligned in zero field, H = 0 (a), and align with the applied field, H > 0 (b), thereby decreasing the magnetic entropy of the system.

This tells us that the reduced magnetic entropy change will be lower in an antiferromagnetic system than in an uncoupled one, as can be seen below, as the spins are not fully saturated below the conditions of lowest temperature and strongest field. The antiferromagnetic coupling in Gd(III)7 is also a hindrance, with behaviour similar to Gd(III)5, when compared to the relevant Brillouin functions. 

Table 6.1 summarizes the thermodynamic parameters relating to the macrocyclic effect for the high-spin Ni(n) complexes of four tetraaza-macrocyclic ligands and their open-chain analogues (the open-chain derivative which yields the most stable nickel complex was used in each case) (Micheloni, Paoletti Sabatini, 1983). Clearly, the enthalpy and entropy terms make substantially different contributions to complex stability along the series. Thus, the small macrocyclic effect which occurs for the first complex results from a favourable entropy term which overrides an unfavourable enthalpy term. Similar trends are apparent for the next two systems but, for these, entropy terms are larger and a more pronounced macrocyclic effect is evident. For the fourth (cyclam) system, the considerable macrocyclic effect is a reflection of both a favourable entropy term and a favourable enthalpy term. 

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