Exchange, energy forces

Bc3 cluster the 3-body forces cannot be approximated solely by the Axilrod-Teller term. The reasons for the satisfactory approximation of many-body energy by the Axilrod-Teller term in the bulk phases of the rare gases were discussed by Meath and Aziz . As follows from precise calculations of the 3-body interaction energy in the Hcg , Neg and Ara trimers, both the Axilrod-Teller and the exchange energies are important. Nevertheless, in some studies of many-body interactions, the exchange effects are still neglected and the many-body contribution is approximated by only dispersion terms, for example see... 

Charge-transfer interactions are attractive forces caused by charge-transfer between an electron donor (with low ionic potential) and an electron acceptor (with high electron affinity)23). Therefore, the potential energy is expressed as shown in Table 1, where ID, Aa, and C denote the ionic potential of the electron donor, the electron affinity of the electron acceptor, the electron exchange energy, and a constant, respectively. 

Entangled states through appropriate interactions can be controlled and forced to exchange energy with surroundings. Because a result of such interactions is a new quantum state, time evolution starts up anew. 

Actually, the only forces between spin are magnetic forces which are exceedingly small and the only reason that spin figures in the answer is that the constraints imposed by the Pauli principle correlate different spin alignments with different electrostatic exchange energies. Thus spin is only an indicator...", J. H. Van Vleck and A. Sherman, Rev. Mod. Phys. 

In the previous three sections we have seen that three different thermodynamic driving forces are associated with three different systems (the NVE, NVT, and NPT systems). The driving forces for the three systems are summarized in Table 1.1. In the simplest case (the NVE system), in which the system does not exchange energy or material with its surroundings, the isolated system moves naturally to... 

However, natural systems consist of flows caused by unbalanced driving forces, and hence the description of such systems requires a larger number of properties in space and time. Such systems are away from the equilibrium state, and are called nonequilibrium systems, they can exchange energy and matter with the environment, and have finite driving forces (Figure 2.1). The formalism of nonequilibrium thermodynamics can describe such systems in a qualitative and quantitative manner by replacing the inequalities of classical thermodynamics with equalities. 

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