Entropy: Why the Universe Tends to Chaos

Why does hot air travel to cooler regions? Why are some processes irreversible? How does the concept of time arise? Why does time only run forwards and not backwards? The concept of entropy and randomness provides the answers to all these questions.

Entropy is a measure of the amount of randomness or chaos within a system. Understanding the way in which this fundamental quantity naturally changes is the key to answering these questions. Systems with high entropy have a high amount of molecular disorder; they lack structure. Since work can be obtained from an orderly molecular structure, systems with lower entropy will have more thermal energy available to be converted into useful forms of work. Contrarily, the thermal energy in systems with high amounts of entropy is largely unavailable for harnessing into useful energy. 

In the study of thermodynamics, the observable, physical properties of a system are known as macroscopic properties. The possible configurations in which the atoms can be arranged, to give rise to a certain macroscopic property, are known as microstates. Each macroscopic property can be described by a certain number of microstates; any system is equally likely to be found in any of its microstates and thus the system will end up in the macrostate that corresponds to most microstates. Entropy can be characterised as the number of possible arrangements that constitute a system and thus it follows that systems naturally tend toward a state of higher entropy.

Second Law of Thermodynamics

The second law of thermodynamics captures this fundamental law of nature, stating that ‘entropy can only increase or remain constant in an isolated system’. The universe is an isolated system, which means it can neither gain nor lose energy; as a result, the second law dictates that the entropy of the universe can only increase or remain constant. The reason behind this lies in statistical mechanics, which revolves around understanding probability.

A Statistical Explanation

Imagine a 1m3 cubic container filled with gas particles and imaginary grids that split the container into 1cm3 cubic volumes. If we heated a corner of the box, a temperature gradient would arise; if we took a snapshot of the molecules after a few seconds, we would find that each cubic segment contains a different total amount of energy, depending on its location in the temperature gradient. If several of the particles escaped their 1cm3 boxes, this temperature gradient would be altered; in other words, there are very few ways in which one could arrange the particles in this snapshot and continue to observe the same macroscopic temperature gradient.

Contrastingly, when the hotter regions of gas move into cooler regions, the more energetic particles distribute their heat energy until there is a constant temperature throughout the system.

As a result, each cubic volume would have approximately the same amount of total energy. No matter how many particles we swapped around, we would continue to observe the same even temperature distribution. There is almost an infinite number of particle arrangements from which an even temperature distribution can arise.

As stated previously, each microstate has an even probability of being observed; if the system has an almost infinite number of microstates that give rise to an even temperature distribution but a limited number that give rise to a temperature gradient, it follows that the system will tend toward the former state with more possible configurations – i.e. the higher entropy state.

In summary, hot regions of gas will be inclined to move toward cooler regions since this configuration has the most amount of microstates associated with it, and thus a probability of occurring. As a result, entropy is increased.

Irreversibility and Reversibility

Entropy increase during a process results in irreversibility. Once 2 or more gases or liquids have been mixed together, they won’t unmix. When you burn a substance, you can’t unburn it. When we burn something, there is a vast amount of heat energy lost to the surroundings – this energy is permanently lost; it cannot be put back into the system to reverse the process. In fact, all physical, natural processes are irreversible as a result of the second law of thermodynamics; there is always at least some energy loss that cannot be recaptured to return to the exact original state. A process is only truly reversible if entropy remains constant; while this doesn’t happen naturally, a carefully moderated isothermal (constant temperature) process can be carried out to get a close approximation.

Time

A famous quote from Steven Hawking reads:

“The increase of disorder or entropy with time 

is one example of what is called an arrow of time, 

something that distinguishes the past 

from the future, giving a direction to time.”

The forward arrow of time, the clear distinction between past and future, is a result of entropy on a large scale. Time is not a fundamental property or a universal truth; on a microscopic level, this construct is violated continuously. The concept of time is a direct consequence of the second law of thermodynamics that is only observed on a macroscopic scale.

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