Entropy

Why does hot objects cool-down and cold object heat-up?

Entropy is the measure of disorder in a closed system. The second law of thermodynamics states that the entropy of a spontaneous system always increases. But why? To understand that we have to know about spontaneous processes. Processes that occur without any external input of energy and continues in the same direction until it reaches its ground state are called spontaneous processes. Cooling of a hot coffee, flattening of a tire, rocks rolling down a hill are some of the examples of a spontaneous process. Now let’s understand entropy. It is mostly related to statistics than thermodynamics. As mentioned, entropy is the disorder of a closed system which refers to the energy distribution in a system. Every closed system consists of atoms that hold the energy of the system in several forms like in their bonds, kinetic energy of the molecules, etc.

We analyze systems using their macro-states which are defined by the properties like pressure, volume, and temperature. Entropy deals with the micro-states of a system which are more precisely defined by the kinetic energies of the molecules, bond energies, etc. Consider preparing a hot cappuccino, after brewing the espresso we add milk which is at a lower temperature. At the molecular level, both the espresso and the milk are mostly made up of water. The hot water molecules of the espresso have high kinetic energy compared to that of milk. When they are mixed the molecules from both the liquids collide and even out. The kinetic energies are averaged which shows that the energy is spread out. Every collision that happened between the molecules results in innumerous microstates. The probability of the temperature of the espresso and milk being averaged is very high that it always happens.

In terms of macro-states, we consider the probabilities of the temperature being averaged, decreased, or increased by knowing the number of microstates that have temperatures averaged, decreased, or increased. As the number of microstates in which the temperature is averaged is very high they form a macro-state in which temperature is averaged. There is a macro-state where the temperature of espresso increases and the temperature of the milk decreases. This has a very low probability that it never happens. A closed system left alone will try out all the microstates but when we measure we always see the high probability macro-state. Everything from burning stars to waterfalls all spontaneous processes you see will always end up with high entropy. It refers to the usable energy in a system. It opposes constricting the energy in a system. Entropy is a big deal due to the inefficiencies it causes to the engines. It defines the flow of time.

Entropy defines the flow of time.

Can the Entropy be reversed?

In 1867 James Clerk Maxwell proposed a thought experiment in which two containers consisting of inert gas molecules that are at high entropy are separated by a wall with a window that can be opened and closed. (Imagine the gas molecules moving and colliding with the walls) Now comes the maxwell’s demon who knows all the properties like the velocities of the gas molecules. When a high-speed molecule reaches the window in the right container he opens the window and let passes the molecule to the left window. When a low-speed molecule reaches the window in the right container he opens the window and let passes the molecule to the right window.

Eventually, all the high-speed molecules are in the right container and all the low-speed molecules end up in the right container. We successfully decreased the entropy of the system. But how? It violates the second law of thermodynamics that entropy of a closed system should always increase. This thought experiment had a flaw in it. The information about the system is stored in the demon and every time he stores and erases the information about the system the entropy of the universe is increased. By storing and erasing every bit of information he increases the entropy of the universe to do that. Hence the law is preserved. Did you notice that we used information and entropy interchangeably? Even the formulas for calculating the entropy and the hidden information of a system are similar.

Blackhole Entropy and The Information Paradox

Black holes are the simplest objects in the universe with basic properties like mass, spin, and charge. As they are very simple their entropy is considered to be zero. The entropy of the materials(stars and other black holes) it feeds is considered to be residing inside the black hole which cannot be accessed by the outside universe but still exits. The energy of the black hole can still be extracted by the Penrose process in which throwing an object into the black hole while being in the ergosphere give us a huge amount of energy in the form of momentum. The problem raised when the Hawking Radiation was discovered. It states that a black hole loses its mass by radiating virtual particles.

The information entropy of the material it fed on is thought to be lost. It violates the information theory that the information cannot be destroyed. Later scientists found a correlation between the entropy of the materials it fed on and the surface area of the event horizon of the black hole. The entropy of the materials it fed on is proportional to the increase in surface area of the event horizon. This led to the discovery of the holographic principle in which the information about the material that entered the event horizon is painted onto its surface. For every plank’s length on the surface area of the event horizon, it stores a single bit of information which is then radiated back into the universe by Hawking Radiation. The holographic principle makes us rethink our reality. It proposes that our 3D universe is nothing but a projected 2D hologram. Scientists later used the Holographic principle to propose string theory.

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