Relationship of macroscopic to microscopic

To relate the observed macroscopic phenomena to various molecular processes is, in general, a task of great difiiculty. Such an undertaking requires a fully developed macroscopic theory to enable proper design and assessment of experimental procedures to be made. Furthermore, without an adequate theory of molecular processes and without a precise relationship between macroscopic and microscopic parameters, it will not be possible to obtain accurate information about events at a molecular level from experimental data. 

It was made clear in the whole symposium that food science has broadened its spectrum of subjects and points of view, from basic to applied aspects, from macroscopic to microscopic and molecular phenomena. The combination of efforts from several disciplines has also advantageously enriched the knowledge on water and its relationships with food components. 

The comparison of the expressions of macroscopic and microscopic constants leads to the following relationships that link them ... 

To further elaborate on this last point, it should be noted that once corpuscular theory is introduced it should provide students with meaningful descriptions, explanations and predictions of macroscopic phenomena and relationships in terms of sub-microscopic entities such as atoms, molecules and electrons. But, alas, according to the foram of experts in chemical education, it does not (Van Berkel et al., 2000). Not only students, but also teachers as well as textbook writers make mistakes with regard to the macro/sub-micro/symbolic levels. Here are some examples mentioned by the international and Dutch fomm. 

How can the curriculum theory described above be useful in effectively applying the two strategies, cormecting to daily-life experiences and updating chemical content, when trying to improve the meaningfulness of learrring with respect to the relationship between macroscopic phenomerra and the sub-microscopic world of atoms and molecrrles ... 

Ben-Zvi, R., Silberstein, J., Mamlok, R. (1990). Macro-micro relationships. A key to the world of chemistry. In R L. Lijnse, et al. (Eds.), Relating macroscopic phenomena to microscopic particles. Utrecht CD-Beta Press. 

The relationship between fluctuation and dissipation is reminiscent of the reciprocal Onsager relations that link affinity to flux. The two relationships become identical under Onsager s regression hypothesis which states that the decay of a spontaneous fluctuation in an equilibrium system is indistinguishable from the approach of an undisturbed non-equilibrium system to equilibrium. The conclusion important for statistics, is that the relaxation of macroscopic non-equilibrium disturbances is governed by the same (linear) laws as the regression of spontaneous microscopic fluctuations of an equilibrium system. In the specific example discussed above, the energy fluctuations of a system in contact with a heat bath at temperature T,... 

We look at the simple gas laws to explore the behaviour of systems with no interactions, to understand the way macroscopic variables relate to microscopic, molecular properties. Finally, we introduce the statistical nature underlying much of the physical chemistry in this book when we look at the Maxwell-Boltzmann relationship. 

Equation 7.35 is a fundamental relationship between the diffusivity and the mean-square displacement of a particle diffusing for a time r. Because diffusion processes in condensed matter are comprised of a sequence of jumps, the mean-square displacement in Eq. 7.31 should be equivalent to Eq. 7.35. This equivalence, as demonstrated below, results in relations between macroscopic and microscopic diffusion parameters. 

The weird properties that came to be associated with quantum systems, because of the probability doctrine, obscured the simple mathematical relationship that exists between classical and quantum mechanics. The lenghthy discussion of this aspect may be of less interest to chemical readers, but it may dispel the myth that a revolution in scientific thinking occured in 1925. Actually there is no break between classical and non-classical systems apart from the relative importance of Planck s action constant in macroscopic and microscopic systems respectively. Along with this argument goes the realization that even in classical mechanics, as in optics, there is a wave-like aspect associated with all forms of motion, which becomes more apparent, at the expense of particle behaviour, in the microscopic domain. 

As this point it is important to differentiate between macroscopic and microscopic surface phenomena. Surface phenomena can be treated macroscopically by chemical thermodynamics, in which atomic concepts are not neccessary. Accordingly, the thermodynamic relationships can be derived on the basis of pressure, volume, surface area, composition, and temperature, which can be measured in a straightforward manner. Historically, therefore, the thermodynamic approach was pursued first. Before discussing the atomic aspects of the energy content of an adsorbate phase we shall briefly summarize the important thermodynamic aspects noting, however, that this cannot be a comprehensive treatment. For the latter we refer to the literature [1, 7, 9-12]. 

This result implies that the energy equipartition relationship of Eq. (2.S) applies as well as the general definitions of Chapter I. Note that for Af m the variable turns out to be coupled weakly to the thermal bath. This condition generates that time-scale separation which is indispensable for recovering an exponential time decay. To recover the standard Brownian motion we have therefore to assiune that the Brownian particle be given a macroscopic size. In the linear case, when M = w we have no chance of recovering the properties of the standard Brownian motion. In the next two sections we shall show that microscopic nonlinearity, on the contrary, may allow that the Markov characters of the standard Brownian motion be recovered with increasing temperature. 

Building a model helps scientists imagine what may be happening at the microscopic level. For this very same reason, the illustrations in this book provide pictures that are models of chemical compounds to help you understand the relationship between the macroscopic and microscopic worlds. Scientists knew that any model they make may have limitations. A model may even have to be modified or discarded as new information is found. This is exactly what happened to scientists models of the atom. 

Fundamental relationship between cosmology and particle physics originates from the well established links between microscopic and macroscopic descriptions in theoretical physics. Remind the links between statistical physics and thermodynamics, or between electrodynamics and theory of electron. To the end of the XX Century the new level of this relationship was realized. It followed both from the cosmological necessity to go beyond the world of known elementary particles in the physical grounds for inflationary cosmology with... 

---