One of the major law of nature is the second law of thermodynamics. Actually, there are altogether four laws of thermodynamics but the second law is the most interesting one. This article is about a thought experiment which seems to violate the second law of thermodynamics! Yes, you heard me right. This sounds like something a flat-earther would say but this thought experiment was devised by none other than the famous physicist, James Clerk Maxwell.
First, Let's get familiar with the second law of thermodynamics.
The total entropy can never decrease over time for an isolated system.
There are many ways of stating the second law but I will stick to this one. The statement above means that heat energy will never flow spontaneously from a cold object to a hotter one. Take a look at the picture below, there are two compartments each with air at a different temperature. The compartments are separated from each other by a thermally insulated wall with a small door, which is closed for now. let's say the blue one is at 10 °C and the red is at 50 °C. What happens when we open the door connecting the compartments? General intuition tells us that the air at 50 °C loses its heat energy to the other one until the system acquires a thermal equilibrium. This "General Intuition" is, in fact, the second law of thermodynamics. The second law is all about the direction of the flow of heat energy. From entropic point of view, the system changes from an ordered state to a disorder one. Up to now, we haven't violated any laws but will the disordered state go back to the ordered on its own? The second law tells us that it won't but Maxwell's demon tries to defy the second law. Yes, in the thought experiment devised by Maxwell, the entropy increases! Before we dive into the thought experiment, we need to understand a bit about the concept of temperature.

Temperature

We relate temperature with hotness and coldness but from a scientific perspective, the words don't have any meaning. A summer day at 40 °C feels hot for us but in comparison with the temperature of the sun, our summer day is too cold. To avoid this relative conundrum, we use a scientific definition of temperature. Quantitatively, we define temperature as:
The measure of the average kinetic energy of molecules.
Kinetic energy is the measure of the vibration and movement of the molecules of a system. In the case of a solid object, the molecules are constantly vibrating and higher the temperature, higher is the amplitude of vibration. Similarly, for a gas, the temperature is the measure of movement of the molecules. This is described by the kinetic theory of gases. The universal scale of temperature measurement, which is the Kelvin scale, is based on this definition of temperature. As the temperature decreases the vibration/movement of molecules decrease and eventually we reach a state when the vibration completely ceases. This temperature is the zero Kelvin.
Kinetic energy is the measure of the vibration and movement of the molecules of a system. In the case of a solid object, the molecules are constantly vibrating and higher the temperature, higher is the amplitude of vibration. Similarly, for a gas, the temperature is the measure of movement of the molecules. This is described by the kinetic theory of gases. The universal scale of temperature measurement, which is the Kelvin scale, is based on this definition of temperature. As the temperature decreases the vibration/movement of molecules decrease and eventually we reach a state when the vibration completely ceases. This temperature is the zero Kelvin.

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Great article! Very informative, pleasant to read.
Since you know a lot about statistical physics, you might like mine about negative Kelvin temperatures :) here
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   2mo ago