Subsystem, dissipative

The previous sections focused on the case of isolated atoms or molecules, where coherence is fully maintained on relevant time scales, corresponding to molecular beam experiments. Here we proceed to extend the discussion to dense environments, where both population decay and pure dephasing [77] arise from interaction of a subsystem with a dissipative environment. Our interest is in the information content of the channel phase. It is relevant to note, however, that whereas the controllability of isolated molecules is both remarkable [24, 25, 27] and well understood [26], much less is known about the controllability of systems where dissipation is significant [78]. Although this question is not the thrust of the present chapter, this section bears implications to the problem of coherent control in the presence of dissipation, inasmuch as the channel phase serves as a sensitive measure of the extent of decoherence. 

The brief review of the newest results in the theory of elementary chemical processes in the condensed phase given in this chapter shows that great progress has been achieved in this field during recent years, concerning the description of both the interaction of electrons with the polar medium and with the intramolecular vibrations and the interaction of the intramolecular vibrations and other reactive modes with each other and with the dissipative subsystem (thermal bath). The rapid development of the theory of the adiabatic reactions of the transfer of heavy particles with due account of the fluctuational character of the motion of the medium in the framework of both dynamic and stochastic approaches should be mentioned. The stochastic approach is described only briefly in this chapter. The number of papers in this field is so great that their detailed review would require a separate article. 

A relaxation process will occur when a compound state of the system with large amplitude of a sparse subsystem component evolves so that the continuum component grows with time. We then say that the dynamic component of this state s wave function decays with time. Familiar examples of such relaxation processes are the a decay of nuclei, the radiative decay of atoms, atomic and molecular autoionization processes, and molecular predissociation. In all these cases a compound state of the physical system decays into a true continuum or into a quasicontinuum, the choice of the description of the dissipative subsystem depending solely on what boundary conditions are applied at large distances from the atom or molecule. The general theory of quantum mechanics leads to the conclusion that there is a set of features common to all compound states of a wide class of systems. For example, the shapes of many resonances are nearly the same, and the rates of decay of many different kinds of metastable states are of the same functional form. 

In many cases of physical interest (e.g., a decay, photoionization, or predissociation) the dynamic and the dissipative subsystems correspond to degenerate (or quasidegenerate) states of the same zero-order Hamiltonian. For future purposes, it will be useful to establish the way in which a metastable state decays in this case. Let the total Hamiltonian for the system be given by... 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

The FrBhlich vibrational model does not address itself directly to ihe problem of the interaction between an external EM-field and the dissipative subsystem, but rather to ihe internal redistribution of photons and phonons upon excitation of the Bose-condensation state. In particular, the frequencies, oo, of the (coherent) vibrations are availalbe only within the framework of a... 

Figure 5. Schematic of an external EM field interaction with the equilibrium system and the dissipative subsystem. a(w) and are the attenuation function and the biological-response function for the equilibrium system, respectively aBIsM and [hns(i ) are the same functions, respectively, for the dissipative subsystem,- m is the frequency of the EM field.

Figure 7. Formal representation of the interaction of an external EM field with the dissipative subsystem in the Frohlich vibrational model (n is the nonlinear coupling parameter (Equation 17) the other quantities have the same meaning as...

There seems to be an agreement to name equation (5) "Exergy". The lost work (called also dissipation),. in a system or a subsystem may also be computed from an "exergy balance" according to equation (6). 

Since is constant, we find that max Sjs corresponds to max(—Gos) and, hence, to min Gos. In turn, attainment of the minimum possible value of the Gibbs energy means the largest feasible useful transformation and the minimum dissipation of the total energy, i.e., the minimum (in this case a zero one) entropy production in the open subsystem. 

Derivation of the expression for the minimum production of S in the systems with constant T and V (volume) differs from the one above only by replacement of enthalpy by internal energy (U) and the Gibbs energy by the Helmholtz energy in the equations. When we set S and P or S and V dissipation turns out to be zero according to the problem statement. In the case of constant U and V or H and P, the interaction with the environment does not hinder the relaxation of the open subsystem toward the state max Sos. 

---