From the thermodynamic point of view, Earth is a closed system, which gets 1.2 x 101 J of energy from the Sun every second in the form of a short-wave radiation, which corresponds to the density of energy flow in 238 Wm-2. The same amount of energy is irradiated into the space in the form of a long-wave (infrared) radiation (see Energy Flows in the Biosphere, Ecological Network Analysis, Environ Analysis, and Energy Balance). We assume that the Earth's total mass and its mean temperature (more precisely, the temperature of the Earth-Atmosphere System (EAS)) are not changing in the course of rather long time (^103 years). The latter means that the planetary radiative balance is constant. These are plausible hypotheses, which can be considered as 'empirical generalizations'.

Carriers of energy are 'hot' photons with temperature Ts = 5800 K of the Sun's surface, and the energy is carried away by 'cooled' photons at TE = 253 K. This is the so-called 'photon mill'; evolution and self-organization of planets (including life on Earth) is a result of its work.

Formally, the photon mill is a typical 'heat machine' functioning as a Carnot cycle, but its working body is the photon gas, whose 'molecules' have no mass, so that in this case it becomes slightly incorrect to talk about a heat machine (although Gibbs has indicated it). Later on, Prigogine stated that such a classic thermodynamic concept as the heat machine is also applicable to the photon gas. Note that this 'roughness' is not necessarily present, if the concept of 'exergy' is used.

Let d^/dt be the internal production of entropy by the EAS, and dec/dt be the exchange flow of entropy between the Sun and the EAS, then the change in the total entropy of the EAS is da dea dia dt dt dt

The value of dec/dtcan be estimated as the algebraic sum of the entropy flow from Sun to Earth, qSE = (4/3) (238 Wm-2) (1/TS), and the entropy flow from the EAS to space, qEs = -(4/3) (238 Wm-2) (1/Te):

V 5800 253

where factor 4/3 is the so-called Planck's form factor. The annual entropic balance for the globe overall is equal to -2 x 1022JK-1yr-1.

We assume here implicitly that the irradiation of the EAS is the blackbody irradiation with TA = TE = 253 K. Indeed, the irradiation is a sum of the blackbody irradiations with the temperatures from 215 to 288 K, so that this estimation is a zero approximation.

In accordance with Prigogine's theorem, at the dynamic equilibrium the system's entropy must be constant, that is, da/dt = 0; whence dea di7 dt dt

The value of dec/dt is known; if we could estimate the value of di^/dt, and if equality [3] holds, or, in other words, if the internal production of entropy is balanced by its export into the environment, we would prove one important statement: the EAS is at the dynamic equilibrium with its environment, the space. Note that equality [3] has to hold overall for the EAS, but each of its subsystems may be in nonequilibrium, so that the main statement of Prigogine's theorem (equality [3]) in relation to each subsystem does not necessarily hold.

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