**7. Condensate of thermal radiation**

Thermal radiation is a unique thermodynamic system while the expression d*U*=*T*d*S*–*p*d*V* for internal energy *U*, entropy *S*, and volume *V* holds the properties of the fundamental

Photons as Working Body of Solar Engines 385

Suppose that the primary medium is radiation and for this medium *U*00,rad–*TS*0*+p*rad*V*=0. Then the condition *U*00,rad<*U*rad*+U*cond is satisfied for values of *p* and *T* necessary for equilibrium. According to this inequality and the Gibbs stability criterion (Muenster, 1970), the medium consisting of the condensate and radiation is stable relatively to primary

In contrary, the equilibrium state of condensate and radiation arises spontaneously from the primary condensate, because *U*00,cond>*U*rad*+U*cond, if *U*00,cond–*TS*0*+p*cond*V*=0. However, the condensate has to lower its energy before the moment of the equilibrium appearance to prevent self-evaporation of medium into radiation. Such a process is possible under any infinitely small local perturbations of the entropy S0. Really, the state of any equilibrium system is defined by the temperature *T* and external parameters (Kondepudi & Prigogin,

While the state of investigated medium is defined by the temperature only, the supposed absence of external forces allows the primary condensate to perform spontaneous adiabatic extension with lowering energy by factor ∆*U*cond=*U*0,cond–*U*00,cond*=p*cond∆*V*. When the energy rest will fulfill the condition *U*0,cond=*U*rad*+U*cond, the required condition *U*0,cond–*TS*0*+p*cond*V*=0

Let's consider the evolution of the condensate being in equilibrium with radiation. Once the medium is appeared, this medium consisting of the equilibrium condensate and radiation can continue the inertial adiabatic extension due to the assumed absence of external forces. When *V*rad≡*V*cond, the second law of thermodynamics can be written as *u=Ts*–*p*, where *u* and *s* are densities of energy and entropy, respectively. Fig. 14 plots a curve of radiation extension as a cubic parabola *s*rad=4σ*T*3/3, where σ is the Stefan-Boltzmann constant. Despite the fact that the density of entropy of the condensate is unknown, we can show it in Fig.1 as a set of positive numbers λ=*Ts*, if each λi is ascribed an equilateral hyperbola *s*cond=λi/*T*.

We include the cross-section point ci of the hyperbola cd and the cubic parabola ab in Fig. 14 in the interval [c0, ck]. Assume the generation of entropy along the line cd outside this interval and the limits of the interval are fixing the boundary of the medium stability. Absence of the entropy generation inside the interval [c0, ck] means that the product

only at *T*0=*T*k=*Ti*. So, if the condensate and radiation are in equilibrium, the equality

Thus, when the equilibrium state is achieved the medium extension is realized along the cross-section line of the parabola and hyperbolas. Equalities *s*cond=*s*rad=4σ*T*3/3 are of fundamental character; all other thermodynamic values for the condensate can be derived

 *u*cond*=Ts*–*p*cond=5σ*T*4/3. (29) For the equilibrium medium consisting of the condensate and radiation *u*cond*=*5*u*rad/3 and *u*0=*u*rad+*u*cond*=*8σ*T*4/3=2λ. For the primary condensate before its extension *u*00=*u*rad+*u*cond– *p=*3σ*T*4. For thermal radiation *u*rad*=*3*p* and the pressure is always positive (Kondepudi &

d*T*(*s*cond+*s*rad). By substituting *s* we can see that these equalities are valid

4/3. For the condensate *u*–*Ts+p*=0 is

radiation, i.e. the condensation of primary radiation is a forced process.

for arising equilibrium between condensate and radiation will be achieved.

1998; Bazarov, 1964; Muenster, 1970).

Fig.14 illustrates both curves.

 *T*k

valid. Then, according to (28),

Prigogin, 1998; Bazarov, 1964).

from these values. For example, we find that λi=4σ*T*<sup>i</sup>

<sup>2</sup>*s*i(*T*k–*T*0) is *T*<sup>0</sup>

*s*cond=*s*rad is also valid.

equation of thermodynamics regardless the variation of the photon number (Kondepudi & Prigogin, 1998. Bazarov, 1964). Differential expression d*p*/d*T*=*S*/*V* for pressure *p* and temperature *T* is valid for one-component system under phase equilibrium if the pressure does not depend on volume *V* (Muenster, 1970). Thermal radiation satisfies these conditions but shows no phase equilibrium.

The determinant of the stability of equilibrium radiation is zero (Semenchenko, 1966). While the "zero" determinants are related to the limit of stability, there are no thermodynamic restrictions for phase equilibrium of radiation (Muenster, 1970). However, successful attempts of finding thermal radiation condensate in any form are unknown. This work aims to support enthusiasm of experimental physicists and reports for the first time the phenomenological study of the thermodynamic medium consisting of radiation and condensate.

It is known (Kondepudi & Prigogin, 1998; Bazarov, 1964), that evolution of radiation is impossible without participating matter and it realizes with absorption, emission and scattering of the beams as well as with the gravitational interaction. Transfer of radiation and electron plasma to the equilibrium state is described by the kinetic equation. Some of its solutions are treated as effect of accumulation in low-frequency spectrum of radiation, as Bose-condensation or non-degenerated state of radiation (Kompaneets, 1957; Dreicer, 1964; Weymann, 1965; Zel'dovich & Syunyaev, 1972; Dubinov А.Е*.* 2009). A known hypothesis about Bose-condensation of relic radiation and condensate evaporation has a condition: the rest mass of photon is thought to be non-zero (Kuz'min & Shaposhnikov, 1978). Nevertheless, experiments show that photons have no rest mass (Spavieri & Rodrigues, 2007).

Radiation, matter and condensate may form a total thermal equilibrium. According to the transitivity principle of thermodynamic equilibrium (Kondepudi & Prigogin, 1998; Bazarov, 1964), participating condensate does not destroy the equilibrium between radiation and matter. Suppose that matter is a thermostat for the medium consisting of radiation and condensate. A general condition of thermodynamic equilibrium is an equality to zero of virtual entropy changes δ*S* or virtual changes of the internal energy δ*U* for media (Bazarov, 1964; Muenster, 1970; Semenchenko, 1966). Using indices for describing its properties, we write *S=S*rad*+S*cond, *U*=*U*rad*+U*cond. The equilibrium conditions δ*S*rad*+*δ*S*cond=0, δ*U*rad+δ*U*cond=0 will be completed by the expression *T*δ*S*=δ*U*+*p*δ*V* , and then we get an equation

$$(\mathbf{1}/T\_{\rm cond}\mathbf{-1}/T\_{\rm rad})\\$IL\_{\rm cond} + (p\_{\rm cond}/T\_{\rm cond})\\$\,V\_{\rm cond} + (p\_{\rm rad}/T\_{\rm rad})\\$\,V\_{\rm rad} = \mathbf{0}.$$

If *V*rad*+V*cond=*V*=const and δ*V*rad= –δ*V*cond, then for any values of variations δ*U*cond and δ*V*cond we find the equilibrium conditions: *T*rad=*T*cond=*T* and *p*rad=*p*cond=*p*. When condensate is absolutely transparent for radiation, it is integrated in condensate, so that *V*rad=*V*cond=*V* and δ*V*rad=δ*V*cond. Thus, conditions

$$T\_{\rm rad} = T\_{\rm cond} \nu \qquad p\_{\rm rad} = - \, p\_{\rm cond} \tag{28}$$

are satisfied for any values of variations δ*U*cond and δ*V*cond.

The negative pressure arises in cases, when *U*–*TS+pV*=0 and *U*>*TS*. We ascribe these expressions to the condensate and assume the existence of the primary medium, for which the expression *S*0*=S*cond+*S*rad is valid in the same volume. Now we try to answer the question about the medium composition to form the condensate and radiation from indefinitely small local perturbations of entropy *S*0 of the medium. Two cases have to be examined.

equation of thermodynamics regardless the variation of the photon number (Kondepudi & Prigogin, 1998. Bazarov, 1964). Differential expression d*p*/d*T*=*S*/*V* for pressure *p* and temperature *T* is valid for one-component system under phase equilibrium if the pressure does not depend on volume *V* (Muenster, 1970). Thermal radiation satisfies these conditions

The determinant of the stability of equilibrium radiation is zero (Semenchenko, 1966). While the "zero" determinants are related to the limit of stability, there are no thermodynamic restrictions for phase equilibrium of radiation (Muenster, 1970). However, successful attempts of finding thermal radiation condensate in any form are unknown. This work aims to support enthusiasm of experimental physicists and reports for the first time the phenomenological study of the thermodynamic medium consisting of radiation and

It is known (Kondepudi & Prigogin, 1998; Bazarov, 1964), that evolution of radiation is impossible without participating matter and it realizes with absorption, emission and scattering of the beams as well as with the gravitational interaction. Transfer of radiation and electron plasma to the equilibrium state is described by the kinetic equation. Some of its solutions are treated as effect of accumulation in low-frequency spectrum of radiation, as Bose-condensation or non-degenerated state of radiation (Kompaneets, 1957; Dreicer, 1964; Weymann, 1965; Zel'dovich & Syunyaev, 1972; Dubinov А.Е*.* 2009). A known hypothesis about Bose-condensation of relic radiation and condensate evaporation has a condition: the rest mass of photon is thought to be non-zero (Kuz'min & Shaposhnikov, 1978). Nevertheless, experiments show that photons have no rest mass (Spavieri & Rodrigues,

Radiation, matter and condensate may form a total thermal equilibrium. According to the transitivity principle of thermodynamic equilibrium (Kondepudi & Prigogin, 1998; Bazarov, 1964), participating condensate does not destroy the equilibrium between radiation and matter. Suppose that matter is a thermostat for the medium consisting of radiation and condensate. A general condition of thermodynamic equilibrium is an equality to zero of virtual entropy changes δ*S* or virtual changes of the internal energy δ*U* for media (Bazarov, 1964; Muenster, 1970; Semenchenko, 1966). Using indices for describing its properties, we write *S=S*rad*+S*cond, *U*=*U*rad*+U*cond. The equilibrium conditions δ*S*rad*+*δ*S*cond=0, δ*U*rad+δ*U*cond=0

If *V*rad*+V*cond=*V*=const and δ*V*rad= –δ*V*cond, then for any values of variations δ*U*cond and δ*V*cond we find the equilibrium conditions: *T*rad=*T*cond=*T* and *p*rad=*p*cond=*p*. When condensate is absolutely transparent for radiation, it is integrated in condensate, so that *V*rad=*V*cond=*V*

 *T*rad = *T*cond, *p*rad = – *p*cond (28)

The negative pressure arises in cases, when *U*–*TS+pV*=0 and *U*>*TS*. We ascribe these expressions to the condensate and assume the existence of the primary medium, for which the expression *S*0*=S*cond+*S*rad is valid in the same volume. Now we try to answer the question about the medium composition to form the condensate and radiation from indefinitely small

will be completed by the expression *T*δ*S*=δ*U*+*p*δ*V* , and then we get an equation

(1/*T*cond–1/*T*rad)δ*U*cond +(*p*cond/*T*cond)δ*V*cond+(*p*rad/*T*rad)δ*V*rad = 0.

local perturbations of entropy *S*0 of the medium. Two cases have to be examined.

but shows no phase equilibrium.

and δ*V*rad=δ*V*cond. Thus, conditions

are satisfied for any values of variations δ*U*cond and δ*V*cond.

condensate.

2007).

Suppose that the primary medium is radiation and for this medium *U*00,rad–*TS*0*+p*rad*V*=0. Then the condition *U*00,rad<*U*rad*+U*cond is satisfied for values of *p* and *T* necessary for equilibrium. According to this inequality and the Gibbs stability criterion (Muenster, 1970), the medium consisting of the condensate and radiation is stable relatively to primary radiation, i.e. the condensation of primary radiation is a forced process.

In contrary, the equilibrium state of condensate and radiation arises spontaneously from the primary condensate, because *U*00,cond>*U*rad*+U*cond, if *U*00,cond–*TS*0*+p*cond*V*=0. However, the condensate has to lower its energy before the moment of the equilibrium appearance to prevent self-evaporation of medium into radiation. Such a process is possible under any infinitely small local perturbations of the entropy S0. Really, the state of any equilibrium system is defined by the temperature *T* and external parameters (Kondepudi & Prigogin, 1998; Bazarov, 1964; Muenster, 1970).

While the state of investigated medium is defined by the temperature only, the supposed absence of external forces allows the primary condensate to perform spontaneous adiabatic extension with lowering energy by factor ∆*U*cond=*U*0,cond–*U*00,cond*=p*cond∆*V*. When the energy rest will fulfill the condition *U*0,cond=*U*rad*+U*cond, the required condition *U*0,cond–*TS*0*+p*cond*V*=0 for arising equilibrium between condensate and radiation will be achieved.

Let's consider the evolution of the condensate being in equilibrium with radiation. Once the medium is appeared, this medium consisting of the equilibrium condensate and radiation can continue the inertial adiabatic extension due to the assumed absence of external forces. When *V*rad≡*V*cond, the second law of thermodynamics can be written as *u=Ts*–*p*, where *u* and *s* are densities of energy and entropy, respectively. Fig. 14 plots a curve of radiation extension as a cubic parabola *s*rad=4σ*T*3/3, where σ is the Stefan-Boltzmann constant. Despite the fact that the density of entropy of the condensate is unknown, we can show it in Fig.1 as a set of positive numbers λ=*Ts*, if each λi is ascribed an equilateral hyperbola *s*cond=λi/*T*. Fig.14 illustrates both curves.

We include the cross-section point ci of the hyperbola cd and the cubic parabola ab in Fig. 14 in the interval [c0, ck]. Assume the generation of entropy along the line cd outside this interval and the limits of the interval are fixing the boundary of the medium stability. Absence of the entropy generation inside the interval [c0, ck] means that the product

<sup>2</sup>*s*i(*T*k–*T*0) is *T*<sup>0</sup> *T*k d*T*(*s*cond+*s*rad). By substituting *s* we can see that these equalities are valid

only at *T*0=*T*k=*Ti*. So, if the condensate and radiation are in equilibrium, the equality *s*cond=*s*rad is also valid.

Thus, when the equilibrium state is achieved the medium extension is realized along the cross-section line of the parabola and hyperbolas. Equalities *s*cond=*s*rad=4σ*T*3/3 are of fundamental character; all other thermodynamic values for the condensate can be derived from these values. For example, we find that λi=4σ*T*<sup>i</sup> 4/3. For the condensate *u*–*Ts+p*=0 is valid. Then, according to (28),

$$
u\_{\rm cond} \equiv \text{Ts-}\mathcal{p}\_{\rm cond} \equiv \text{5oT4}^{\bullet}/\mathcal{B}.\tag{29}$$

For the equilibrium medium consisting of the condensate and radiation *u*cond*=*5*u*rad/3 and *u*0=*u*rad+*u*cond*=*8σ*T*4/3=2λ. For the primary condensate before its extension *u*00=*u*rad+*u*cond– *p=*3σ*T*4. For thermal radiation *u*rad*=*3*p* and the pressure is always positive (Kondepudi & Prigogin, 1998; Bazarov, 1964).

Photons as Working Body of Solar Engines 387

a fixed energy density 4 GeV/m³ is supposed to be the origin of the cosmological acceleration. The nature of this phenomenon is unknown (Chernin, 2008; Lukash & Rubakov, 2008; Green, 2004) . What part of this energy can have a relic condensate

The relic condensate according to (29) has the energy density 4 GeV/m³ when the temperature of relic radiation is about 27 К. If the accelerated extension of the cosmological medium arises at *T*\* ≤ 27 К, the part of energy of the relic condensate in the total energy of the cosmological medium is (*T*\*/27)4. According to the Fridman model *T*\* corresponds to the red shift ≈0.7 (Chernin, 2008) and temperature 4.6 К. Then the relic condensate can have

As a conclusion one should note that the negative pressure of the condensate of thermal radiation is Pascal-like and isotropic, it is constant from the moment as the equilibrium with radiation was disturbed by the condensate and is equal (by absolute value) to the energy density with precision of additive constant. The condensate of thermal radiation is a physical medium which interacts only with the radiation and this physical medium penetrates the space as a whole. This physical medium cannot be obtained under laboratory conditions because there are always external forces for a thermodynamic system in laboratory. While this paper was finalized the information (Klaers et al., 2009) showed the photon Bose-condensate can be obtained. This condensate has no negative pressure while it is localized in space. It seems very interesting to find in the nature a condensate of thermal radiation with negative pressure. Possible forms of physical medium with negative pressure and their appearance at cosmological observations are widely discussed. The radiation can consist of other particles, then the photon, among them may be also unknown particles. We hope that modelling the medium from the condensate and radiation will be useful for checking the hypotheses and will allow explaining the nature of the substance responsible for accelerated extension of the Universe. The medium from thermal radiation and condensate is the first indication of the existence of physical vacuum as one of the subjects in

classical thermodynamics and the complicated structure of the dark energy.

of the contact: dark current, which is unknown for metals, was detected.

**8. Electrical properties of copper clusters in porous silver of silicon solar** 

Technologies for producing electric contacts on the illuminated side of solar cells are based on chemical processes. Silver technologies are widely used for manufacturing crystalline silicon solar cells. The role of small particles in solar cells was described previously (Hitz, 2007; Pillai, 2007; Han, 2007; Johnson, 2007). The introduction of nanoparticles into pores of photon absorbers increases their efficiency. In our experiments copper microclusters were chemically introduced into pores of a silver contact. They changed the electrical properties

In the experiments, we used 125 x×125-mm commercial crystalline silicon wafers Si<P>/SiNx (70 nm)/Si<B> with a silver contact on the illuminated side. The silver contact was porous silver strips 10–20 μm thick and 120–130 μm wide on the silicon surface. The diameter of pores in a contact strip reached 1μm. The initial material of the contact was a silver paste (Dupont), which was applied to the silicon surface through a tungsten screen mask. After drying, organic components of the paste were burned out in an inert atmosphere at 820–960° C. Simultaneously, silver was burned in into silicon through a 70 nm-thick silicon nitride layer. After cooling in air, the wafer was immersed in a copper salt

accounting the identical equation of state *u* = – *p* for both media?

a 0.1% part of the cosmological medium.

**cells** 

The extension of the medium is an inerial process, so that the positive pressure of radiation *p*rad lowers, and the negative pressure of the condensate *p*cond increases according to the condition (1). Matter is extended with the medium. As it is known in cosmological theory (Kondepudi & Prigogin, 1998; Bazarov, 1964), the plasma inertial extension had led to formation of atoms and distortion of the radiation-matter equilibrium. Further local unhomogeneities of matter were appeared as origins of additional radiation and, consequently, matter created a radiation excess in the medium after the equilibrium radiation-matter was disturbed This work supposes that radiation excess may cause equilibrium displacement for the medium, thus radiation and condensate will continue extending inertially in a non-equilibrium process.

Fig. 14. Schematically plots the density of entropy for radiation (curve *ab*) and for a condensate (curves *cd* and *ef*). The positive pressure of the radiation and negative pressure of condensate are equal by absolute value at the points ci and ek at the interceptions of these curves.

We assume that the distortion of the equilibrium radiation-condensate had been occurred at the temperature *T*i of the medium at the point ci in Fig. 14. The radiation will be extended adiabatically along the line ciа of the cubic parabola without entropy generation. While the condition *V*rad=*V*cond is satisfied if the equilibrium is disturbed, the equality *s*cond=*s*rad points out directions of the condensate extension without entropy generation. As it is shown in Fig.14, the unchangeable adiabatic isolation is possible if the condensate extends along the isotherm *T*i without heat exchange with radiation. Differentiation of the expression *U*cond– *T*i*S*cond*+p*cond*V*=0 with *T*=const and *S=*const gives that *p*cond is also constant.

The medium as a whole extends in such a manner that the positive pressure *p*rad of radiation decreases, and the negative pressure *p*\*cond remains constant. As radiation cools down, the ratio *p*\*/*p*rad lowers, the dominant *p*\* of the negative pressure arises, and the medium begins to extend with positive acceleration.

The thermodynamics defines energy with precision of additive constant. If we assume this constant to be equal to *TS*cond, then the equality *u*\*cond*=U*\*cond/*V* = –*p*\*cond, is valid; this equality points out the fixed energy density of the condensate under its expansion after distortion of the medium equilibrium.

The space is transparent for relic radiation which is cooling down continuously under adiabatic extension of the Universe. Assuming existence of the condensate of relic radiation we derive an expression for a fixed energy density of the condensate *u*\* with the beginning of accelerated extension of the Universe. The adiabatic medium with negative pressure and

The extension of the medium is an inerial process, so that the positive pressure of radiation *p*rad lowers, and the negative pressure of the condensate *p*cond increases according to the condition (1). Matter is extended with the medium. As it is known in cosmological theory (Kondepudi & Prigogin, 1998; Bazarov, 1964), the plasma inertial extension had led to formation of atoms and distortion of the radiation-matter equilibrium. Further local unhomogeneities of matter were appeared as origins of additional radiation and, consequently, matter created a radiation excess in the medium after the equilibrium radiation-matter was disturbed This work supposes that radiation excess may cause equilibrium displacement for the medium, thus radiation and condensate will continue

e

a0

condensate

c

c0

f

b

radiation

2*Ti*


Temperature, *T* Fig. 14. Schematically plots the density of entropy for radiation (curve *ab*) and for a condensate (curves *cd* and *ef*). The positive pressure of the radiation and negative pressure of condensate

We assume that the distortion of the equilibrium radiation-condensate had been occurred at the temperature *T*i of the medium at the point ci in Fig. 14. The radiation will be extended adiabatically along the line ciа of the cubic parabola without entropy generation. While the condition *V*rad=*V*cond is satisfied if the equilibrium is disturbed, the equality *s*cond=*s*rad points out directions of the condensate extension without entropy generation. As it is shown in Fig.14, the unchangeable adiabatic isolation is possible if the condensate extends along the isotherm *T*i without heat exchange with radiation. Differentiation of the expression *U*cond–

The medium as a whole extends in such a manner that the positive pressure *p*rad of radiation decreases, and the negative pressure *p*\*cond remains constant. As radiation cools down, the ratio *p*\*/*p*rad lowers, the dominant *p*\* of the negative pressure arises, and the medium begins

The thermodynamics defines energy with precision of additive constant. If we assume this constant to be equal to *TS*cond, then the equality *u*\*cond*=U*\*cond/*V* = –*p*\*cond, is valid; this equality points out the fixed energy density of the condensate under its expansion after

The space is transparent for relic radiation which is cooling down continuously under adiabatic extension of the Universe. Assuming existence of the condensate of relic radiation we derive an expression for a fixed energy density of the condensate *u*\* with the beginning of accelerated extension of the Universe. The adiabatic medium with negative pressure and

are equal by absolute value at the points ci and ek at the interceptions of these curves.

*T*i*S*cond*+p*cond*V*=0 with *T*=const and *S=*const gives that *p*cond is also constant.

to extend with positive acceleration.

distortion of the medium equilibrium.

a d

ci

extending inertially in a non-equilibrium process.

entropy density, *s*

a fixed energy density 4 GeV/m³ is supposed to be the origin of the cosmological acceleration. The nature of this phenomenon is unknown (Chernin, 2008; Lukash & Rubakov, 2008; Green, 2004) . What part of this energy can have a relic condensate accounting the identical equation of state *u* = – *p* for both media?

The relic condensate according to (29) has the energy density 4 GeV/m³ when the temperature of relic radiation is about 27 К. If the accelerated extension of the cosmological medium arises at *T*\* ≤ 27 К, the part of energy of the relic condensate in the total energy of the cosmological medium is (*T*\*/27)4. According to the Fridman model *T*\* corresponds to the red shift ≈0.7 (Chernin, 2008) and temperature 4.6 К. Then the relic condensate can have a 0.1% part of the cosmological medium.

As a conclusion one should note that the negative pressure of the condensate of thermal radiation is Pascal-like and isotropic, it is constant from the moment as the equilibrium with radiation was disturbed by the condensate and is equal (by absolute value) to the energy density with precision of additive constant. The condensate of thermal radiation is a physical medium which interacts only with the radiation and this physical medium penetrates the space as a whole. This physical medium cannot be obtained under laboratory conditions because there are always external forces for a thermodynamic system in laboratory. While this paper was finalized the information (Klaers et al., 2009) showed the photon Bose-condensate can be obtained. This condensate has no negative pressure while it is localized in space. It seems very interesting to find in the nature a condensate of thermal radiation with negative pressure. Possible forms of physical medium with negative pressure and their appearance at cosmological observations are widely discussed. The radiation can consist of other particles, then the photon, among them may be also unknown particles. We hope that modelling the medium from the condensate and radiation will be useful for checking the hypotheses and will allow explaining the nature of the substance responsible for accelerated extension of the Universe. The medium from thermal radiation and condensate is the first indication of the existence of physical vacuum as one of the subjects in classical thermodynamics and the complicated structure of the dark energy.
