RF/Microwave Interaction Mechanisms in Biological Materials - RF/Microwave Interaction with Biological Tissues - page 79

2.4 ENERGY

A simple medium, such as a lossless dielectric medium, exhibits no dispersion;
that is, its electrical characteristics do not vary with frequency. In this case, the
EM energy has an exact thermodynamic significance: It is the difference
between the internal energy per unit volume with and without the field, respec-
tively, with unchanged density and entropy. In the presence of dispersion,
however, no such simple interpretation is possible. Moreover, in the general
case of arbitrary dispersion, the EM energy cannot be rationally defined as a
thermodynamic quantity [36]. This is because the presence of dispersion in
general signifies a dissipation of energy, which is the reason why a dispersive
medium is also an absorbing medium.
To determine this dissipation under a single-frequency EM excitation, one
averages with respect to time the rate of change of energy in unit volume of
the body. This yields the steady rate of change of the energy, which is the mean
quantity Q of heat evolved per unit time and volume. It has been shown in
Section 1.4 that the imaginary parts of determine the absorption (dis-

sipation) of energy. These imaginary parts are associated with the electric and
magnetic losses, respectively. On account of the law of increase of entropy, the
sign of these losses is determinate: The dissipation of energy is accompanied
by the evolution of heat, that is, Q

e and m

> 0 . It therefore follows from Poynting's

theorem that the imaginary parts of e and m are always positive,

e ¢¢ > 0 m ¢¢ > 0 (2.5)

for all substances in thermal equilibrium and at all frequencies. If the body is
not in thermal equilibrium, then Q may in principle be negative. The second
law of thermodynamics requires only a net increase in entropy as a result of
the effects of the variable EM field and the absence of thermodynamic equi-
librium, the latter effect being independent of the presence of the field. On
the other hand, the signs of the real parts of e and m for w ≠ 0 are subject to

no physical restriction.
Any nonsteady process in an actual body is to some extent thermodynam-
ically irreversible. The electric and magnetic losses in a variable EM field
therefore always occur to some extent, however slight. That is, the functions
e≤

) are not exactly zero for any frequency other than zero, which
does not exclude the possibility of only very small losses in certain frequency
ranges. These ranges are then called transparency ranges and the material is
said to be transparent in these frequency ranges. It is possible to neglect the
absorption in these ranges and to introduce the concept of internal energy of
the body in the EM field in the same sense as in a constant field. To determine
this, it is not sufficient to consider an EM source of only one single frequency,
since the strict periodicity results in no steady accumulation of EM energy.
One then considers a field whose components have frequencies in a narrow

( w ) and m≤ ( w