Energy is the backbone of the universe, with entropy its architect. Although the laws of thermodynamics establish the rules of existence through defining equilibrium and the conservation of matter, the Second Law distinguishes itself as the most consequential. It is the 'arrow' of modern physics, dictating how all systems move toward disorder. From the impossibility of perpetual motion to the eventual heat death of the universe, entropy is the underlying mechanism that ensures the irreversibility of the universe. The gravity of it is best captured by Pope: 'Thy hand, great Anarch! lets the curtain fall; And universal darkness buries all.' 

Entropy is the measure of how ‘spread out’ energy is. Imagine a battery. All the energy is concentrated in the battery, and the energy is usable. However, in the universe, all energy wants to spread out. Now imagine a radiator. The radiator dissipates heat over a large distance; the heat is not useful as once it has been spread out, so the energy has been degraded. Similarly, when a battery is plugged into a circuit, its energy goes to the components, each of which heat up and dissipate heat into the surroundings (all energy ends up as heat). Think about a cup of coffee left in a room. The concentrated heat slowly spreads out to the room, until it has the same temperature as the room (maximum entropy). This principle is integral to all interactions in the world. 

Centuries before the concept of entropy, Da Vinci once noted how "no machine can continue to move itself indefinitely [perpetual motion]”. While this quote is on the nature of friction, the deeper reality is explained by entropy. The energy in a closed system (a system where no energy can be put in or taken out) remains the same (conservation of energy), yet the usability of it declines over time.

Entropy goes beyond just a measure of disorder. It explains why cold things heat up, why hot things cool down, why ink mixed into water swirls to make mesmerising patterns before vanishing into homogeneity, how perfume fills a room with sweet-smelling aromas. Beyond this, it also causes the statistical noise of DNA that drives ageing in humans. Some believe that life itself is birthed from its exceptional ability to turn low entropy (useful energy) into high entropy (non-useful energy). Ideas derived from entropy arise in economics and cryptography, and are foundational to the internet, encryption and the markets.

In order to visualise why energy tends to high entropy, we need to look at statistical mechanics. Statistical mechanics is related to the workings of a larger system, not its subcomponents. Many systems have phenomena that are unable to be described by simply looking at the particles within it (this is also known as emergence), and can only be explained when you zoom out. In the same way you can’t understand the concept of ‘wetness’ just by looking at water molecules, or understand consciousness through neurons, you need to look at heat transfer from afar to understand it. 

Picture two metal bars, with 20 atoms each, laid out in a grid. One bar has 12 energy ‘packets’ (hot) and the other has 5 (cold). Every second (in actual systems, the time period is much shorter), the packets move. They move randomly, either to different atoms in the bar, or ‘jump’ across one bar to the other (cold to hot or hot to cold). For this model, we are assuming that one atom can only hold one energy packet (though this is not the case). The shifting packets make lots of different configurations, each one equally as likely. This seems like it would be a contradiction, as random motion could mean that even more energy ends up in the hot bar from the cold bar.

There are 422,814,600 different states where the hot bar ends up with more energy than when it started. That is massive. However, computing the number of states that the heat doesn’t increase gives us 8.87x1010 states, which is significantly larger. The probability that heat moves from cold to hot is 0.00477. For reference, it is similar in probability to rolling three sixes, one after another. As the number of particles and energy ‘packets’ in the systems grow, the probability shrinks down until it is infinitesimally small. Therefore, though it is never impossible for a hot object to gain energy from a cold one, it is so unlikely that it almost never happens, and when it does happen, after another second, the energy packets move again, meaning that it only heats for a fleeting moment. Because of this, all systems tend to equilibrium.In order to convey this concept, below is a specially made Python Notebook that can be played around with to get a feel of this probabilistic system. Through entering the size of the hot and cold bars, as well as their respective number of packets, it computes the total number of states where heat increases, as well as providing a look at the probability distribution. It also describes the maths behind the numbers given.

However, entropy describes more than just the disorderedness of a system; it provides a direction for the universe itself. Entropy is a unidirectional process, you cannot add order to chaos, only chaos to order. Therefore, time must also be unidirectional, as it is the driving force behind entropy. This 'arrow of time' ensures that the processes we observe are irreversible, distinguishing the past from the future. Entropy also characterises how the universe will end (in our understanding).

Everything in the universe relies on gradients (the change in energy between two points). For example, a hot cup of coffee has a thermal energy gradient with the surroundings: they are not in thermal equilibrium. When that gradient has fully decayed, both are the same temperature, and entropy is at a maximum. Similarly, a battery contains a chemical gradient where one side has a higher concentration of ions than the other. When the battery is placed into a circuit, the ions move to the other side to balance it out, moving to a system of maximum entropy. All gradients decay. 

On a universal scale, this means that there will be a point where there are no longer any gradients, the universe has reached its most homogeneous, probable state. When all the stars fade and all the black holes die (by the releasing of Hawking radiation), there will be no more gradients, and therefore, no more ‘excitement’, nothing interesting will happen again. Time will be directionless, there is no distinction between the past, the present and the future. The universe will have died.