Macrosystem

The NAs such as DNA usually used in the experiments consist of 10" -1 o nucleotides. Thus, they should be considered as macrosystems. Moreover, in experiments with wet NA samples macroscopic quantities are measured, so averaging should also be performed over all nucleic acid molecules in the sample. These facts justify the usage of the macroscopic equations like (3) in our case and require the probabilities of finding macromolecular units in the certain conformational state as variables of the model. 

One may attempt to approximate to such an experimental situation by considering a subsystem with small dimensions in the direction of the flow, so that a single temperature may be sufficiently precise in describing it. In this model one would have to provide a time-dependent hamiltonian operating in such a way as to feed energy into the system at one boundary and to remove energy from the other boundary. We would therefore be obliged to discuss systems with hamiltonians that are explicitly functions of time, and also located on the boundaries of the macrosystem. 

All discussions of transport processes currently available in the literature are based on perturbation theory methods applied to kinetic pictures of micro-scattering processes within the macrosystem of interest. These methods do involve time-dependent hamiltonians in the sense that the interaction operates only during collisions, while the wave functions are known only before and after the collision. However these interactions are purely internal, and their time-dependence is essentially implicit the over-all hamiltonian of the entire system, such as the interaction term in Eq. (8-159) is not time-dependent, and such micro-scattering processes cannot lead to irreversible changes of thermodynamic (ensemble average) properties. 

A physically acceptable theory of electrical resistance, or of heat conductivity, must contain a discussion of the explicitly time-dependent hamiltonian needed to supply the current at one boundary and remove it at another boundary of the macrosystem. Lacking this feature, recent theories of such transport phenomena contain no mechanism for irreversible entropy increase, and can be of little more than heuristic value. 

Liquid liquid interfaces occur as macro- and also as micro- and nanoheterogenous systems (termed small systems), described in colloidal chemistry as, e.g., miscelles, vesicles, and microemulsions [14,19] (see also Section V). Up to now, fast progress concerns mainly the macrosystems (> 100/rm), including all types of natural and artificial membranes. 

Figure 1.5. Schematic of a fully integrated macroelectronic system and an example of an application concept for macroelectronic systems, (a) Building blocks for a generic macrosystem, (b) Mockup of a large-area antenna array. [Figure courtesy of Sarnoff Corporation. Used with permission.]...

Systems of chemical interest typically contain particles in molar quantity. Mathematical modelling of all interactions in such a system is clearly impossible. Even in a system of non-interacting particles, such as an ideal gas, it would be equally impossible to keep track of all individual trajectories. It is consequently not a trivial matter to extend the mechanical description (either classical or non-classical) of single molecules to macrosystems. It would be required in the first place to define the initial state of each particle in terms of an equation... 

The only known alternatives for the analysis of macrosystems are by the phenomenological approach, known as thermodynamics, or by the use of... 

The observations on which thermodynamics is based refer to macroscopic properties only, and only those features of a system that appear to be temporally independent are therefore recorded. This limitation restricts a thermodynamic analysis to the static states of macrosystems. To facilitate the construction of a theoretical framework for thermodynamics [113] it is sufficient to consider only systems that are macroscopically homogeneous, isotropic, uncharged, and large enough so that surface effects can be neglected, and that are not acted on by electric, magnetic or gravitational fields. The only mechanical parameter to be retained is the volume V. For a mixed system the chemical composition is specified in terms of the mole numbers Ni, or the mole fractions [Ak — 1,2,..., r] of the chemically pure components of the system. The quantity V/(Y j=iNj) is called the molar... 

The most important new concept to come from thermodynamics is entropy. Like volume, internal energy and mole number it is an extensive property of a system and together with these, and other variables it defines an elegant self-consistent theory. However, there is one important difference entropy is the only one of the extensive thermodynamic functions that has no obvious physical interpretation. It is only through statistical integration of the mechanical behaviour of microsystems that a property of the average macrosystem, that resembles the entropy function, emerges. 

To put the previous statement into perspective it is necessary to stipulate that any macrosystem with well-defined values of its extensive parameters is made up of myriads of individual particles, each of which may be endowed with an unspecified internal energy, within a wide range consistent with all external constraints. The instantaneous distribution of energy among the constituent particles, adding up to the observed macroscopic energy, defines a microstate. It is clear that any given macrostate could arise as the result of untold different microstates. 

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