The law of entropy and the second law of thermodynamics...
Wikipedia said:
In physical cosmology, assuming that nature is described by a Grand unification theory, the grand unification epoch was the period in the evolution of the early universe following the Planck epoch, starting at about 10^{-43} seconds after the Big Bang, in which the temperature of the universe was comparable to the characteristic temperatures of grand unified theories. If the grand unification energy is taken to be 10^{15} GeV, this corresponds to temperatures higher than 10^{27} K. During this period, three of the four fundamental interactions—electromagnetism, the strong interaction, and the weak interaction—were unified as the electronuclear force. Gravity had separated from the electronuclear force at the end of the Planck era.
During the Grand Unification Epoch, physical characteristics such as mass, charge, flavour and colour charge were meaningless. The grand unification epoch ended at approximately 10^{-36}seconds after the Big Bang. At this point several key events took place. The strong force separated from the other fundamental forces. The temperature fell below the threshold at which X and Y bosons could be created, and the remaining X and Y bosons decayed.[citation needed] It is possible that some part of this decay process violated the conservation of baryon number and gave rise to a small excess of matter over antimatter (see baryogenesis). This phase transition is also thought to have triggered the process of cosmic inflation that dominated the development of the universe during the following inflationary epoch.
Wikipedia said:
Baryon asymmetry parameter
The challenges to the physics theories are then to explain how to produce this preference of matter over antimatter, and also the magnitude of this asymmetry. An important quantifier is the asymmetry parameter,
\eta = \frac{n_B - n_{\bar B}}{n_\gamma}.
This quantity relates the overall number density difference between baryons and antibaryons (n_B and n_{\bar B}, respectively) and the number density of cosmic background radiation photons n_{\gamma}.
According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly 3,000 kelvin, corresponding to an average kinetic energy of 3,000 K / (10.08×10^4 K/eV) = 0.3 \; \text{eV}. After the decoupling, the total number of CBR photons remains constant. Therefore due to space-time expansion, the photon density decreases. The photon density at equilibrium temperature T, per cubic kelvin and per cubic centimeter, is given by
n_{\gamma} = \frac{1}{\pi^2} {\left(\frac{k_B T}{\hbar c}\right)}^3 \int_0^\infty \frac{x^2}{\exp(x) - 1} dx \simeq 20.3 \left(\frac{T}{1\text{K}}\right)^3 \text{cm}^{-3}
with k_B as the Boltzmann constant, \hbar as the Planck constant divided by 2 \pi and c as the speed of light in vacuum. At the current CBR photon temperature of 2.725 \; \text{K}, this corresponds to a photon density n_{\gamma} of around 4^{11} CBR photons per cubic centimeter.
Therefore, the asymmetry parameter \eta, as defined above, is not the "good" parameter. Instead, the preferred asymmetry parameter uses the entropy density s,
\eta_s = \frac{n_B - n_{\bar B}}{s}
because the entropy density of the universe remained reasonably constant throughout most of its evolution. The entropy density is
s \ \stackrel{\mathrm{def}}{=}\ \frac{\mathrm{entropy}}{\mathrm{volume}} = \frac{p + \rho}{T} = \frac{2\pi^2}{45}g_{*}(T) T^3
with p and \rho as the pressure and density from the energy density tensor T_{\mu \nu} and g^{*} as the effective number of degrees of freedom for "massless" particles (if mc^2 \ll k_B T holds) at temperature T,
g_{*} (T) = \sum_\mathrm{i=bosons} g_i{\left(\frac{T_i}{T}\right)}^3 + \frac{7}{8}\sum_\mathrm{j=fermions} g_j{\left(\frac{T_j}{T}\right)}^3
for bosons and fermions with g_i and g_j degrees of freedom at temperatures T_i and T_j respectively. At the present era, s = 7.04 \cdot n_{\gamma}.
Wikipedia said:
The second law of thermodynamics is an expression of the universal principle of decay observable in nature. It is measured and expressed in terms of a property called entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium; and that the entropy change dS of a system undergoing any infinitesimal reversible process is given by δq / T, where δq is the heat supplied to the system and T is the absolute temperature of the system.
Entropy (arrow of time)
Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system will increase when no extra energy is consumed. Hence, from one perspective, entropy measurement can be thought of as a kind of clock—although not really an accurate measure of time.
Physical processes at the microscopic level are believed to be either entirely or mostly time symmetric, meaning that the theoretical statements that describe them remain true if the direction of time is reversed; yet when we describe things at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time. An arrow of time is anything that exhibits such time-asymmetry.
The largest contributor to the entropy budget of the Universe is super massive black holes.
Schwarzschild radius:
R_s = \frac{2GM}{c^2}
Schwarzschild black hole sphere surface area:
A_s = 4 \pi R_s^2 = 4 \pi \left( \frac{2GM}{c^2} \right)^2 = \frac{16 \pi G^2 M^2}{c^4}
Planck radius:
r_P = \sqrt{\frac{\hbar G}{c^3}}}
Schwarzschild black hole entropy integration by substitution:
S_{BH} = \frac{dE}{dT} = k_B \ln \Omega_s = k_B \left( \frac{A_s}{4 r_P^2} \right) = \frac{k_B}{4} \left( \frac{16 \pi G^2 M^2}{c^4} \right) \left( \frac{c^3}{\hbar G} \right) = \frac{4 \pi k_B G}{\hbar c} M^2
Schwarzschild black hole entropy:
\boxed{S_{BH} = \frac{4 \pi k_B G}{\hbar c} M^2}
Entropy of the Universe:
S_u = \sum_{i = 1}^{n} S_i = k_B \ln \Omega_u
S_u = 3.1 \cdot 10^{104} \; \frac{\text{j}}{\text{K}}
\boxed{\ln \Omega_u = \frac{S_u}{k_B} = 2.245 \cdot 10^{127}}
\Omega_u - number of equally probable states in the Universe
The law of entropy and the second law of thermodynamics are more fundamental laws in the Universe than those involved with symmetry breaking events such as the phase transition of Planck epoch energy to baryonic matter, grand unification theory, matter over antimatter asymmetry and the Standard Model, etc., because those two laws were in effect prior to these epochs in the Universe during the Planck epoch, when the dimensions of space-time and energy and possible equally probable states were generated.
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Reference:
Second law_of_thermodynamics - Wikipedia
http://en.wikipedia.org/wiki/Boltzmann%27s_constant"
http://en.wikipedia.org/wiki/Entropy_%28arrow_of_time%29"
http://en.wikipedia.org/wiki/Arrow_of_time"
http://en.wikipedia.org/wiki/Grand_unification_epoch"
http://en.wikipedia.org/wiki/Baryogenesis#Baryon_asymmetry_parameter"
http://en.wikipedia.org/wiki/Black_hole_thermodynamics#Black_hole_entropy"
http://theastronomist.fieldofscience.com/2009/09/entropy-of-universe.html"
http://en.wikipedia.org/wiki/Schwarzschild_radius#Formula_for_the_Schwarzschild_radius"
http://en.wikipedia.org/wiki/Planck_length#Value"
