**4.1 Photon reemissions as non-working processes**

Matter and solar radiation are never in equilibrium in solar cells and quasi-static conversion of the solar energy is not achieved. For this reason, the irreversible thermodynamic engines are described using the method of endoreversible thermodynamics of solar energy conversion (Novikov, 1958; Rubin, 1979; De Vos, 1992). Remember that endoreversible engines are irreversible engines where all irreversibilities are restricted to the coupling of engine to the external world. It is assumed that the inner reversible part of an еndoreversible engine is a Carnot cycle. We have also considered the non-Carnot cycles and found out that photon absorption in solar cells can be considered as the external reversible part of an еndoreversible engine.

The photon absorption in solar cells is separated into processes with and without work production. These processes are sequencies of transitions from one energy state of the system to another. The energy transitions between particle states are called "photon reemission" if they do not take part in performing work and heat dissipation.

The photon reemission is divided into reversible and irreversible processes. These nonworking processes are regarded as a continuous series of equilibrium states outside the irreversible or endoreversible engine, are isolate into separate processes, and are used to obtain a higher efficiency of the generally non-quasistatic solar energy conversion. We can consider those equilibrium processes as a base of the "exoreversible"additional device for the irreversible or endoreversible engine.

So, we have called the processes without work production photon reemission. Let us now shown that they play a special role in the conversion of solar heat into work.

### **4.2 Antenna states of the absorber particles**

Let us consider these particle states in a radiant energy absorber, transitions between them result from the absorption of photons. The states of atomic particles or their groups, as well as energy transitions between them, are called "working" if they take part in performing work. It is known that solar energy conversions are not always working processes. The states of atomic particles and the energy transitions between them are said to be "antenna" ones if they take part in the absorption and emission of radiant energy without work production, i.e. in the photon reemission. Carnot cycles are examples of working processes, while cycles described below involving the photon reemission are examples of antenna processes.

Photons as Working Body of Solar Engines 373

difference can be used to divide all processes with the absorption and generation of photons into two types. The first type includes processes in which the matter and radiation do work, that is, participate in the working process. The second type includes processes in which the substance absorbs and emits radiant energy without doing work, that is, participates in an antenna process. The spontaneous evening out of the temperatures of the matter and radiation is an example of antenna processes, and radiant energy conversion in a solar cell is

The highest efficiency of a combination of work and antenna processes is described by the line AB in Fig. 8. If the work is performed during a non-Carnot cycle then efficiency of the work and antenna processes is described by the LB line. The difference between *η*OS*η*U and *η*L is 94.8-93.1=1.7%. For analysis of antenna processes one should choose the temperature

The CEB line in Fig.9 shows the efficiency of a combination of work done by matter (in a Carnot cycle with the efficiency *η*0), by radiation (in a non-Carnot cycle with the efficiency *η*AS) and a background antenna process with the efficiency *η*U. The *η* coordinates of the CEB line divided by *η*L describe the largest contribution of working processes to the efficiency of solar energy conversion if *η*L is taken as one. The contribution of the antenna process is then

It follows that the efficiency of conversion higher than *η*0*η*AS*η*U (the region between the LB and CEB lines, Fig. 9) can be obtained by perfecting the antenna process only. The efficiency of solar energy conversion is maximum in this case if all antenna processes are reversible.

The *η* coordinates of points between the LB and CEB lines are then proportional to the fraction of reversible antenna processes. An irreversible antenna process corresponds to the 1 - *η*/*η*L value. The character of this dependence will not be discussed here. Only note that Fig. 9 can be used to calculate the fractions of work and antenna processes, as well as contributions of reversible and irreversible antenna processes in solar energy conversion if experimental data on the temperature dependence of the solar cell efficiency are

So, the antenna processes in Landsberg engine are reversible. When antenna processes are made irreversible, then the efficiency of transformation of radiant energy decreases from

The notion of the reversibility of a process is applicable to any thermodynamic system, although we have not found it applied to quantum systems in physical literature. Let us recall that the transition of a system from equilibrium state 1 to equilibrium state 2 is called reversible (i.e., bi-directional) if one can return from state 2 to state 1 without making any changes in the surrounding environment, i.e. without compensations. The transition of a system from state 1 to state 2 is said to be irreversible if it is impossible to return from state 2

Let us consider these particle states in an absorber, transitions between them result from the absorption of photons. The state of radiation will not change if the photon reemissions (121) or (12321) can take place (Fig. 10). These reemission processes will be reversible ones if the equilibrium state of matter is not violated by a photon absorption. According to these definitions, the reemission (123) or (1231) will alter the frequency distribution of photons

*η*L=94.8% down to *η*0*η*AS*η*U=5.79% at *Т*A=320 К. We have to select the opposite way.

dependence of the value *η*L because in this case a conversion process is reversible.

The efficiency is minimum if all antenna processes are irreversible.

**4.4 Photon reemissions as reversible antenna processes** 

(Fig. 11). For this reason, such reemission processes are irreversible.

to state 1 without compensations.

a combination of processes of the first and second type.

1- *η*0*η*AS*η*U/*η*L.

available.

It is clear that antenna and working states are equilibrium ones if cycles of the radiant energy conversion are not accompanied by entropy production, i.e. if it takes place along line LB on Fig. 9 with an efficiency *μ*L from Eq. (5). Let us take their total amount to be 100%. Now assume that the conversion of radiant energy consists of reversible working processes with an efficiency *μ*О from Eq. (2) for matter, with an efficiency *μ*AS from Eq. (5) for radiation and irreversible with an efficiency *μ*U from Eq. (1) for irreversible antenna processes, i.e. that the conversion of radiant energy corresponds to line CEB. In this case, the *μ*-coordinates of all points belonging to the line CEB divided by *μ*L are equal to the fraction of working states, while 1-*μ*/*μ*L is equal to the fraction of antenna non-equilibrium states.

Fig. 9 shows that the number of antenna non-equilibrium states in solar cells decreases as the efficiency *μ* grows along lines CE and CF. The isothermal growth of the efficiency *μ* implies that the total amount of antenna states remains constant, but certain antenna states have become equilibrium states and that reversible transitions that do not generate work have appeared. If the temperature dependence of *μ* is determined by experiment, Fig. 9 becomes in our opinion an effective tool for interpreting and modeling the paths along which work is performed by solar cells. We can consider Fig. 9 as the reversibility diagram of the conversion of solar heat into work.

Fig. 9. Comparison of the efficiency *μ* L of Landsberg engine (the LB line) with the efficiencies of combined engines (the CEB, CFB lines). A difference between the efficiencies *η*0*η*AS*η*U and *μ*O*μ*C*μ*U is that in the first case radiation working cycle is not a Carnot cycle. Lines CEB and CFB are practically coincide at temperatures used for operation of solar cells.

Obviously, knowledge of physical and chemical nature of antenna states of particles is important for revealing optimal schemes for radiant energy conversion. The question about technical realization of antenna states is not subject of this chapter. This is a material science problem. One only should note the model of absorber with antenna states does not contradict to thermodynamic laws and represents a way of solution of following aim: how to separate any given cycle into infinite number of infinitely small arbitrary cycles.

#### **4.3 Antenna processes**

The absorption and generation of photons in the abcd (Fig. 2) and spet (Fig. 4) processes is accompanied by the production of work. No work is done in the st process (Fig. 2). This

It is clear that antenna and working states are equilibrium ones if cycles of the radiant energy conversion are not accompanied by entropy production, i.e. if it takes place along line LB on Fig. 9 with an efficiency *μ*L from Eq. (5). Let us take their total amount to be 100%. Now assume that the conversion of radiant energy consists of reversible working processes with an efficiency *μ*О from Eq. (2) for matter, with an efficiency *μ*AS from Eq. (5) for radiation and irreversible with an efficiency *μ*U from Eq. (1) for irreversible antenna processes, i.e. that the conversion of radiant energy corresponds to line CEB. In this case, the *μ*-coordinates of all points belonging to the line CEB divided by *μ*L are equal to the fraction of working states,

Fig. 9 shows that the number of antenna non-equilibrium states in solar cells decreases as the efficiency *μ* grows along lines CE and CF. The isothermal growth of the efficiency *μ* implies that the total amount of antenna states remains constant, but certain antenna states have become equilibrium states and that reversible transitions that do not generate work have appeared. If the temperature dependence of *μ* is determined by experiment, Fig. 9 becomes in our opinion an effective tool for interpreting and modeling the paths along which work is performed by solar cells. We can consider Fig. 9 as the reversibility diagram

Fig. 9. Comparison of the efficiency *μ* L of Landsberg engine (the LB line) with the

to separate any given cycle into infinite number of infinitely small arbitrary cycles.

The absorption and generation of photons in the abcd (Fig. 2) and spet (Fig. 4) processes is accompanied by the production of work. No work is done in the st process (Fig. 2). This

efficiencies of combined engines (the CEB, CFB lines). A difference between the efficiencies *η*0*η*AS*η*U and *μ*O*μ*C*μ*U is that in the first case radiation working cycle is not a Carnot cycle. Lines CEB and CFB are practically coincide at temperatures used for operation of solar cells. Obviously, knowledge of physical and chemical nature of antenna states of particles is important for revealing optimal schemes for radiant energy conversion. The question about technical realization of antenna states is not subject of this chapter. This is a material science problem. One only should note the model of absorber with antenna states does not contradict to thermodynamic laws and represents a way of solution of following aim: how

while 1-*μ*/*μ*L is equal to the fraction of antenna non-equilibrium states.

of the conversion of solar heat into work.

**4.3 Antenna processes** 

difference can be used to divide all processes with the absorption and generation of photons into two types. The first type includes processes in which the matter and radiation do work, that is, participate in the working process. The second type includes processes in which the substance absorbs and emits radiant energy without doing work, that is, participates in an antenna process. The spontaneous evening out of the temperatures of the matter and radiation is an example of antenna processes, and radiant energy conversion in a solar cell is a combination of processes of the first and second type.

The highest efficiency of a combination of work and antenna processes is described by the line AB in Fig. 8. If the work is performed during a non-Carnot cycle then efficiency of the work and antenna processes is described by the LB line. The difference between *η*OS*η*U and *η*L is 94.8-93.1=1.7%. For analysis of antenna processes one should choose the temperature dependence of the value *η*L because in this case a conversion process is reversible.

The CEB line in Fig.9 shows the efficiency of a combination of work done by matter (in a Carnot cycle with the efficiency *η*0), by radiation (in a non-Carnot cycle with the efficiency *η*AS) and a background antenna process with the efficiency *η*U. The *η* coordinates of the CEB line divided by *η*L describe the largest contribution of working processes to the efficiency of solar energy conversion if *η*L is taken as one. The contribution of the antenna process is then 1- *η*0*η*AS*η*U/*η*L.

It follows that the efficiency of conversion higher than *η*0*η*AS*η*U (the region between the LB and CEB lines, Fig. 9) can be obtained by perfecting the antenna process only. The efficiency of solar energy conversion is maximum in this case if all antenna processes are reversible. The efficiency is minimum if all antenna processes are irreversible.

The *η* coordinates of points between the LB and CEB lines are then proportional to the fraction of reversible antenna processes. An irreversible antenna process corresponds to the 1 - *η*/*η*L value. The character of this dependence will not be discussed here. Only note that Fig. 9 can be used to calculate the fractions of work and antenna processes, as well as contributions of reversible and irreversible antenna processes in solar energy conversion if experimental data on the temperature dependence of the solar cell efficiency are available.

So, the antenna processes in Landsberg engine are reversible. When antenna processes are made irreversible, then the efficiency of transformation of radiant energy decreases from *η*L=94.8% down to *η*0*η*AS*η*U=5.79% at *Т*A=320 К. We have to select the opposite way.

### **4.4 Photon reemissions as reversible antenna processes**

The notion of the reversibility of a process is applicable to any thermodynamic system, although we have not found it applied to quantum systems in physical literature. Let us recall that the transition of a system from equilibrium state 1 to equilibrium state 2 is called reversible (i.e., bi-directional) if one can return from state 2 to state 1 without making any changes in the surrounding environment, i.e. without compensations. The transition of a system from state 1 to state 2 is said to be irreversible if it is impossible to return from state 2 to state 1 without compensations.

Let us consider these particle states in an absorber, transitions between them result from the absorption of photons. The state of radiation will not change if the photon reemissions (121) or (12321) can take place (Fig. 10). These reemission processes will be reversible ones if the equilibrium state of matter is not violated by a photon absorption. According to these definitions, the reemission (123) or (1231) will alter the frequency distribution of photons (Fig. 11). For this reason, such reemission processes are irreversible.

Photons as Working Body of Solar Engines 375

The radiant energy conversion may be characterized by the variable ratio of numbers of reversible and irreversible processes. In the chain (7) this ratio depends on (as shown in Figs. 10, 11) the order of states 1, 2, 3 alternation in cycle of each particle **А**. The index of **А** points it out. In general case we do not know either the reemission number, or states number in the cycle of reemission, as well as their alternation. But formally we can make a continuum consisting of all reversible cycles of the chain (7) and photons of reemission. Separate the

(**А**1→2→1 + *hυ*21 + **А**1→3→1 + *hυ*31 + **А**2→3→2 + *hυ*32 + .....) +

The sequence of particles states in brackets may be thought as infinite one. (Note that if only one particle were in the brackets, then manifold repetition of its cycle might be considered as an infinite sequence of equilibrium states). In the solid absorber one can select a big number (~1019) of chains consisting of these particles. While the quasistatic process is by definition an infinite and continous sequence of equlibrium states, then there is a fundamental possibility to consider local quasistatic processes in the whole irreversible

Thus the sequences of photon reemissions of absorber particles in solar cells can take the form of quasi-static processes. Their isolation out from the general process of the conversion of solar energy into work (which is a non-equilibrium process on the whole) does not

Let us call the reemission of solar energy during an antenna process *retranslation*, if the temperature of the radiation remains constant, and *transformation*, if the temperature of the radiation changes. The retranslation of radiation by a black body is, by definition, a reversible process. Transformation can take place both in a reversible and irreversible way. Therefore, the efficiency of the work performed by a solar cell can be improved by increasing the fraction of retranslating and transforming reversible antenna processes as

A photon cutting process (Wegh et al., 1999) as photon reemission is an example for an antenna process. It includes the emission of two visible photons for each vacuum ultraviolet photon absorbed. For us important, that materials with introduced luminescent activators ensure the separation of the photon antenna reemissions and the photon work production processes. In our opinion, ultra-high efficiencies can be reached if: firstly, we solve the problem of separating the photon antenna reemissions and the photon work production processes. Secondly, one should know a way of transformation of irreversible photon antenna reemissions into reversible. Let us consider the activator states in an absorber as state 3. A photon cutting process is irreversible in case of the reemissions (1231)n. They can be luminescent. A photon cutting process can be reversible if an activator performs the reemissions (1231321)n. They cannot be luminescent. An absorber with such activators can resemble a black body. Therefore, photon cutting processes can also play a role in transformation of irreversible reemission into reversible. This way is one of many others.

**А**1→2→3→1 + *hυ*23 + *hυ*31 + **А**1→3→2→1 + *hυ*32 + *hυ*21 (8)

reversible cycles and photons by brackets and right down the following expression:

The particles with irreversible reemission cycles are out of brackets.

process of radiant energy transformation.

contradict the laws of thermodynamics.

**4.6 Antenna processes and temperature of radiation** 

well as working equilibrium states in an absorber.

**4.7 Antenna processes and photon cutting** 

Fig. 10. The reversible reemissions in the systems with 2 and 3 energy levels.

Fig. 11. The irreversible reemissions in the systems with 3 energy levels.

#### **4.5 Photon reemissions as quasi-static process**

Every quasi-static process is reversible and infinitely slow. Are the continuous series of the photon reemissions (121)n and (12321)n quasi-static processes? For the sake of simplicity, let us approximate the spatial arrangement of particles by a periodic chain of elements that have a length of 2µm (absorber thickness) and that are separated by 2 Å (atomic distance). Use the identity of electronic states 1, 2, 3 in particles **А** and present the sequence of electronic excitations in the particles' chain with help of reemission cycles in the Figs. 10, 11, for example, as follows:

$$\begin{array}{c} \mathbf{A}\_{1} + l\mathbf{w}\_{12} \xrightarrow{\cdot} \\ \rightarrow \mathbf{A}\_{1\to 2\to 1} + l\mathbf{w}\_{21} \xrightarrow{\cdot} \\ \rightarrow \mathbf{A}\_{1\to 2\to 3\to 1} + l\mathbf{w}\_{23} + l\mathbf{w}\_{31} \xrightarrow{\cdot} \\ \rightarrow \mathbf{A}\_{1\to 3\to 1} + l\mathbf{w}\_{31} \xrightarrow{\cdot} \\ \rightarrow \mathbf{A}\_{1\to 3\to 2\to 1} + l\mathbf{w}\_{21} \xrightarrow{\cdot} \dots \\ \rightarrow \mathbf{A}\_{1\to 2\to 1} + l\mathbf{w}\_{21} \end{array} \tag{7}$$

In this expression the first particle is excited by the photon with energy *hυ* 21 and emits the same photon. This emitted photon excites the second particle, which emits two photons with energies *hυ*23 and *hυ*31. They, in turn, excite the third particle and so on.

The time period during which solar radiation will excite only the first particle in the chain, while subsequent particles are excited only by reemitted photons, is equal to 10-4 s if the lifetime of the excited state is ~10-8 s. The time needed for the wave to travel down the chain and excite only the last particle is ~10-14 s. These time intervals are related to each other as 320 years to one second. Therefore, the energy exchange due to reemission in a chain of particles is an infinitely slow process in comparison with the diffusion of electromagnetic radiation in the chain. Even the multiple repetition of reemission (121) by one particle during ~10-6 s is an infinitely slow process, the time taken by such reemission exceeds the lifetime of the excited states by a factor of 100.

Fig. 10. The reversible reemissions in the systems with 2 and 3 energy levels.

Fig. 11. The irreversible reemissions in the systems with 3 energy levels.

Every quasi-static process is reversible and infinitely slow. Are the continuous series of the photon reemissions (121)n and (12321)n quasi-static processes? For the sake of simplicity, let us approximate the spatial arrangement of particles by a periodic chain of elements that have a length of 2µm (absorber thickness) and that are separated by 2 Å (atomic distance). Use the identity of electronic states 1, 2, 3 in particles **А** and present the sequence of electronic excitations in the particles' chain with help of reemission cycles in the Figs. 10, 11,

**4.5 Photon reemissions as quasi-static process** 

→**А**1→2→3→1+*hυ*23+*hυ*31→

lifetime of the excited states by a factor of 100.

→**А**1→3→1+*hυ*31→

energies *hυ*23 and *hυ*31. They, in turn, excite the third particle and so on.

→**А**1→3→2→1+*hυ*21→ ....

→ **А**1→2→1 +*hυ*21 (7)

In this expression the first particle is excited by the photon with energy *hυ* 21 and emits the same photon. This emitted photon excites the second particle, which emits two photons with

The time period during which solar radiation will excite only the first particle in the chain, while subsequent particles are excited only by reemitted photons, is equal to 10-4 s if the lifetime of the excited state is ~10-8 s. The time needed for the wave to travel down the chain and excite only the last particle is ~10-14 s. These time intervals are related to each other as 320 years to one second. Therefore, the energy exchange due to reemission in a chain of particles is an infinitely slow process in comparison with the diffusion of electromagnetic radiation in the chain. Even the multiple repetition of reemission (121) by one particle during ~10-6 s is an infinitely slow process, the time taken by such reemission exceeds the

for example, as follows:

→**А**1→2→1+*hυ*21→

**А**1+*hυ*12→

The radiant energy conversion may be characterized by the variable ratio of numbers of reversible and irreversible processes. In the chain (7) this ratio depends on (as shown in Figs. 10, 11) the order of states 1, 2, 3 alternation in cycle of each particle **А**. The index of **А** points it out. In general case we do not know either the reemission number, or states number in the cycle of reemission, as well as their alternation. But formally we can make a continuum consisting of all reversible cycles of the chain (7) and photons of reemission. Separate the reversible cycles and photons by brackets and right down the following expression:

$$\mathbf{A} \left( \mathbf{A}\_{1 \to 2 \to 1} + h\nu\_{21} + \mathbf{A}\_{1 \to 3 \to 1} + h\nu\_{31} + \mathbf{A}\_{2 \to 3 \to 2} + h\nu\_{32} + \dots \right) +$$

$$\mathbf{A}\_{1 \to 2 \to 3 \to 1} + h\nu\_{23} + h\nu\_{31} + \mathbf{A}\_{1 \to 3 \to 2 \to 1} + h\nu\_{32} + h\nu\_{21} \tag{8}$$

The particles with irreversible reemission cycles are out of brackets.

The sequence of particles states in brackets may be thought as infinite one. (Note that if only one particle were in the brackets, then manifold repetition of its cycle might be considered as an infinite sequence of equilibrium states). In the solid absorber one can select a big number (~1019) of chains consisting of these particles. While the quasistatic process is by definition an infinite and continous sequence of equlibrium states, then there is a fundamental possibility to consider local quasistatic processes in the whole irreversible process of radiant energy transformation.

Thus the sequences of photon reemissions of absorber particles in solar cells can take the form of quasi-static processes. Their isolation out from the general process of the conversion of solar energy into work (which is a non-equilibrium process on the whole) does not contradict the laws of thermodynamics.

### **4.6 Antenna processes and temperature of radiation**

Let us call the reemission of solar energy during an antenna process *retranslation*, if the temperature of the radiation remains constant, and *transformation*, if the temperature of the radiation changes. The retranslation of radiation by a black body is, by definition, a reversible process. Transformation can take place both in a reversible and irreversible way. Therefore, the efficiency of the work performed by a solar cell can be improved by increasing the fraction of retranslating and transforming reversible antenna processes as well as working equilibrium states in an absorber.

### **4.7 Antenna processes and photon cutting**

A photon cutting process (Wegh et al., 1999) as photon reemission is an example for an antenna process. It includes the emission of two visible photons for each vacuum ultraviolet photon absorbed. For us important, that materials with introduced luminescent activators ensure the separation of the photon antenna reemissions and the photon work production processes. In our opinion, ultra-high efficiencies can be reached if: firstly, we solve the problem of separating the photon antenna reemissions and the photon work production processes. Secondly, one should know a way of transformation of irreversible photon antenna reemissions into reversible. Let us consider the activator states in an absorber as state 3. A photon cutting process is irreversible in case of the reemissions (1231)n. They can be luminescent. A photon cutting process can be reversible if an activator performs the reemissions (1231321)n. They cannot be luminescent. An absorber with such activators can resemble a black body. Therefore, photon cutting processes can also play a role in transformation of irreversible reemission into reversible. This way is one of many others.

Photons as Working Body of Solar Engines 377

where μm is a chemical potential of heat radiation emitted by product P. Then the calculation of the function *f*(*T*) is simply reduced to the definition of a difference (μm–μS), because chemical potential of heat radiation does not depend on chemical composition of the radiator, and the numerical procedure for μm and μS is known and simple (Laptev, 2008). The chemical potential as an intensive parameter of the fundamental equation of thermodynamics is defined by differentiation of characteristic functions on number of particles *N* (Laptev, 2010). The internal energy *U* as a characteristic function of the photon number

*U*(*V,N*) = (2.703*N*k)4/3/(σ*V*)1/3 is calculated by the author in (Laptev, 2008, 2010) by a joint solution of two equations: the

*U*(*S*,*V*) = σ *V*(3*S/4* σ *V*)4/3

 *N* = 0.370 σ*T* 3*V*/k = *S /* 3.602 k, (12) where *T*, *S*, *V* are temperature, entropy and volume of heat radiation, σ is the Stephan– Boltzmann constant, *k* is the Boltzmnn constant. In total differential of *U*(*V*, *N*) the partial

( *U N* )*<sup>V</sup>* ≡ heat radiation = 3.602*kT* (13)

introduces a temperature dependence of chemical potential of heat radiation (Laptev, 2008, 2010). The function *U*(*S*, *V*, *N*) is an exception and is not a characteristic one because of the

The Sun is a total radiator with the temperature *T*S = 5800 K. According to (13), the chemical potential of solar radiation is 3.602*kT* = 173.7 kJ/mol. Then the difference *f*(*T*) = μm – μS is a function of the matter temperature *T*m. For example, *f*(*T*) = –165.0 kJ/mol when *T*m = 298.15 K, and it is zero when *T*m = *T*S. According to (13), the function *f*(*T*) can be presented as

According to the Carnot theorem, this factor coincides with the efficiency of the Carnot

 *f*(*T*)/ *S* = – ηс (*Тm* , *TS* ) (14) can characterize an efficiency of the idealized Carnot engine-reactor in known limit

In the heat engine there is no process converting heat into work without other changes, i.e. without compensation. The energy accepted by the heat receiver has the function of compensation. If the working body in the heat engine is a heat radiation with the limit temperatures *T*m and *T*S, then the compensation is presented by the radiation with temperature *T*m which is irradiated by the product P at the moment of its formation. We will call this radiation a compensation one in order to make a difference between this radiation

(Bazarov, 1964) and the expression (Couture & Zitoun, 2000; Mazenko, 2000)

known characteristic function

derivative

relationship (12).

proportional to the dimensionless factor:

engine ηC(*Т*m, *T*S). Then the function

temperatures *T*m and *T*S.

and heat radiation of matter.

 *f*(*T*) = *<sup>m</sup>* – *<sup>S</sup>* = – *<sup>S</sup>* (1–*Tm / TS*).

μR –μP = μm –μS = *f*(*T*), (11)

### **4.8 Antenna processes in plants**

Let us leave the discussion of technological matters relating to the manipulation of antenna processes aside for the time being. We will devote a subsequent publication to this subject. Let us only remark here that the conversion of solar energy involving the participation of antenna molecules figures in the description of photosynthesis in biology. Every chlorophyll molecule in plant cells, which is a direct convertor of solar energy, is surrounded by a complex of 250- 400 pigment molecules (Raven et al., 1999). The thermodynamic aspects of photosynthesis in plants were studied in (Wuerfel, 2005; Landsberg, 1977), yet the idea of antenna for solar cells was not proposed. We hope that the notions of the antenna and working states of an absorber particles will make it possible to attain very high efficiencies of the radiant energy convertors, especially in those cases when solar radiation is not powerful enough to make solar cells work efficiently yet suffices to drive photosynthesis in plants.

### **4.9 Conclusion**

This leads us to conclude that reemission of radiant energy by absorbent particles can be considered a quasi-static process. We can therefore hope that the concept of an antenna process, which is photon absorption and generation, can be used to find methods for attaining the efficiency of solar energy conversion close to the limiting efficiency without invoking band theory concepts.
