The Misunderstood Nature of Entropy

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Entropy and the second law of thermodynamics have been credited with defining the arrow of time, predicting the ultimate heat death of the universe, and providing the driving force for the development of structure as well as decay, and also excusing the messiness of your room. But what is entropy really, and how fundamental is it to our universe?

Entropy is surely one of the most intriguing and misunderstood concepts in all of physics. The entropy of the universe must always increase, so says the second law of thermodynamics. It's a law that seems emergent from deeper laws. It's statistical in nature, and yet may ultimately be more fundamental and unavoidable than any other law in physics. Einstein said that the thermodynamics that encapsulates the second law is the only physical theory of universal content which I am convinced will never be overthrown.

And the great astrophysicist, Sir Arthur Eddington, warned, if your theory is found to be against the second law of thermodynamics, I can give you no hope. There is nothing for it but to collapse in deepest humiliation. We've looked at entropy in the past, but it's time to go much deeper, to unravel the great unraveller.

Over some upcoming episodes, we'll explore different aspects and consequences of entropy, including its role in black hole thermodynamics and how it will lead to the end of our universe. But today, we'll see what entropy really is and why the second law of thermodynamics is considered to be so fundamental and so unavoidable. Let's start from the beginning. In 1824, Sadi Kano published his Reflections on the Motive Power of Fire, in which he revealed the theory for perfect engine efficiency. Heat engines, which in Kano's day were the newfangled steam engines, work by turning the flow of heat energy into mechanical energy. For heat to flow, you need two reservoirs of different temperature. A perfectly efficient engine, one undergoing the Kano cycle, converts all transferred heat energy into useful work. In principle, that work can then be converted back into heat, and so the temperature differential can be reestablished. However, an inefficient engine will slowly deplete the difference in temperature, reducing the heat flow, and the engine winds down. Around a half century after Kano, Rudolf Clausius was inspired to quantify this tendency of heat energies to decay over time. Enter entropy. Clausius defined entropy as the internal property that changes as heat energy moves around within a system.

Specifically, the change in entropy of each reservoir is the heat energy going into or out of that reservoir divided by its temperature. For a Kano cycle, the overall change in entropy is zero. But for any less efficient cycle, entropy increases. In fact, an increase in entropy means that the heat reservoirs are approaching the same temperature, reducing their capacity to do useful work. Kano and Clausius' work revealed entropy as a measure of how evenly spread out a system's energy is. The more evenly spread, the less useful the energy is. And for an isolated system, the best you can hope for is that the separation of energy and the entropy remain constant. In reality, it will almost always increase unless energy comes in from the outside to reestablish the temperature differential. This understanding of entropy is in terms of flowing heat. And it came from the days when many, including Kano himself, believed that heat was a physical fluid called caloric. It took a revolution to understand the reality of entropy. That revolution was statistical mechanics, founded by the great Ludwig Boltzmann with his kinetic theory of gases.

This theory explained thermodynamic behavior as-