There is no off ramp :)

Mirror Beach

S = entropy

k_{b} = Boltzmann constant

\ln = natural logarithm

\Omega = number of microscopic configurations

Being rather limited in math to say the least, this "simple" equation explains in a way even I can understand as entropy is the driving engine of the 2nd law of thermodynamics. When paired with the first, the two define reality as being an environment sustained by the ever moving essence of energy.

Entropy is a measure of disorder. It corresponds with how many possible microscopic configurations can underlie an overall state.

Heat flowing from hot water to cold water

The First Law: Energy can neither be created or destroyed, only transformed

The Second Law: Isolated systems spontaneously evolve towards thermal equilibrium 

—the state of maximum entropy/disorder.

The rabbit hole beckons. :)

Exactly 200 years ago, a French engineer introduced an idea that would quantify the universe’s inexorable slide into decay. But entropy, as it’s currently understood, is less a fact about the world than a reflection of our growing ignorance. Embracing that truth is leading to a rethink of everything from rational decision-making to the limits of machines.

Sadi Carnot,  aged 17 in the uniform of a cadet of the École polytechnique.
Portrait by Louis-Léopold Boilly (1813).

Factoid: Reading through Carnot’s book a few decades later, in 1865, the German physicist Rudolf Clausius coined a term for the proportion of energy that’s locked up in futility. He called it “entropy,” after the Greek word for transformation. He then laid out what became known as the second law of thermodynamics: “The entropy of the universe tends to a maximum.”

But it's more than that ...

Rudolf Clausius (left) originated the insight that entropy tends to increase. Ludwig Boltzmann rooted this rise in statistical mechanics. Theo Schafgans (left); Creative Commons

Physicists of the era erroneously believed that heat was a fluid (called “caloric”). Over the following decades, they realized heat was rather a byproduct of individual molecules bumping around. This shift in perspective allowed the Austrian physicist Ludwig Boltzmann to reframe and sharpen the idea of entropy using probabilities.

Heisenberg's Uncertainty Principle & Entropy, a match make in heaven

Claude Shannon

Entropy experienced a rebirth during World War II. Claude Shannon, an American mathematician, was working to encrypt communication channels, including the one that connected Franklin D. Roosevelt and Winston Churchill. That experience led him to think deeply about the fundamentals of communication over the following years. Shannon sought to measure the amount of information contained in a message. He did so in a roundabout way, by treating knowledge as a reduction in uncertainty.

In essence, entropy's an information construct as per John Wheeler's From It to Bit

From John Wheeler (1983), Law Without Law. In: Quantum theory and measurement.

"It from bit symbolizes the idea that every item of the physical world has at bottom — at a very deep bottom, in most instances — an immaterial source and explanation; that what we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and this is a participatory universe. 

The limits of knowledge rules

An illustration of M4, the sponge after four iterations of the construction process

We will never know everything but you already know that, right? Georg Cantor proved this to be so with infinities residing within infinities using his theory of transfinite numbers to make it happen. The Menger Sponge, seen above, is a 3D representation of Cantor's theory.

In closing ...

Low

High

In closing ...

“Nothing in life is certain except death, taxes and the second law of thermodynamics,” wrote(opens a new tab) Seth Lloyd, a physicist at the Massachusetts Institute of Technology. There’s no sidestepping this directive. The growth of entropy is deeply entwined with our most basic experiences, accounting for why time runs forward and why the world appears deterministic rather than quantum mechanically uncertain.

But despite its fundamental importance, entropy is perhaps the most divisive concept in physics. “Entropy has always been a problem,” Lloyd told me. The confusion stems in part from the way the term gets tossed and twisted between disciplines — it has similar but distinct meanings in everything from physics to information theory to ecology. But it’s also because truly wrapping one’s head around entropy requires taking some deeply uncomfortable philosophical leaps.

Everything's connected and entangled, this is why we rubes have a consistent view of a "uncertain" reality we will never fully understand. Awesome to a fault without question if you're one willing to question. :)

And so it goes ... K. Vonnegut