Entropy and the Initial Conditions of Universe

The concept of entropy is one of the most fascinating concepts. Aside from the implications for thermodynamics, it may also determine the reality of how the universe unraveled. And no one can be fascinated upon realization after taking a nice course on thermodynamics.

The concept of entropy was put precisely into practice by Austrian physicist Ludwig Boltzmann at the end of the nineteenth century. He showed that entropy is a measure of disorder. The greater the disorder, the greater the entropy. So, entropy is not something physical that is added to the universe. And what has been disordered? The rise in disorder of all the energy and matter in the universe. The concept of entropy is everywhere in our everyday lives. According to the second law of thermodynamics, the entropy of the system always tends to its maximum;

dSuni > 0.


This awesome expression lets us come to the profound realization that anything that is ordered at the beginning keeps on diminishing, and it’s irreversible. It can’t be destroyed, as it’s the law by which the universe as a whole functions. For example, glasses shatter into numerous pieces upon being dropped on the ground, and the gas escapes from the ballon when released or blasted. But, if the shatters can’t gather themselves to make glass again, so can the gas inside the balloon. The energy that we exploit, like the burning of wood in a cold, snowy winter, into heat and light, which turns into ash and gases, can’t be brought back to wood. Rather, we have increased the randomness of molecules (the arrangement of molecules in solids is more ordered than in gases), which is entropy.


As we continue using all energy, there will be a time when all the matters have lost their orderliness, meaning energy is not usable anymore. The universe, which is believed to have been formed from the Big Bang, has undergone an increase in entropy, creating space-time. And that is why we find a place to exist in the fabric of the endless cosmos. The initial condition of the Big Bang was a low-entropy [1] macro-state because it produced a mostly hydrogen universe at low temperature [3]. There wouldn't be any stars, planets, or life if the cosmos had come into being in a high-entropy, equilibrium condition. A closed, isolated thermodynamic system's "arrow of time" is produced by low-entropy states that progress to higher entropy. Because high-entropy systems are unpredictable and we are aware that the cosmos is moving toward greater entropic states, we can't predict the future or evaluate the past. The amount of free energy still available in the universe to power all processes is shown by the difference in entropy between the universe's maximum and actual entropies. When the entropy gap becomes zero, it reaches the point of heat death [2].

Fig: The Entropy of the Universe as a Function of Time. Suni(t) monotonically increases. We define Smax  as a constant equal to the largest entropy that the universe will ever have, Suni =Smax. We define the entropy gap as DS(t) =Smax-Suni(t).


While it is unsure that the low entropy of the universe is localized to our region of space and other universes might contain much higher entropy (close to approx. to Smax), our observation in a homogenous universe (greater than 100 light-scale radii, the universe is homogenous) has found no anomaly. The gravitational entropy is observed to be as low as ours. The fate of fragile life as it depends on the entropy and initial conditions of the universe is just puzzling and overwhelming to think about.


References


[1] Lineweaver, C.H., Egan, C.: Life, gravity and the second law of thermodynamics. Phys. Life Rev. 5, 225–242 (2008)

[2] Lineweaver, C.H.: A simple treatment of complexity: cosmological entropic boundary conditions on increasing complexity. In: Edt Lineweaver, C.H., Davies, P.C.W., Ruse, M.

(eds.) Complexity and the Arrow of Time, Cambridge University Press, pp. 42–67 (2013)

[3] Sharpe, C. F., Barnes, L. A., & Lewis, G. F. (2023). On cosmological low entropy after the big bang: Universal Expansion and nucleosynthesis. General Relativity and Gravitation, 55(2), 1–13. https://doi.org/10.1007/s10714-023-03090-y 



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