In the tumult of the industrial revolution, while steam engines were transforming the European landscape, a young 28-year-old polytechnician published a work which initially went unnoticed. On the banks of the Seine, in 1824, Sadi Carnot proposed in his Thoughts on the motive power of fire a mathematical analysis which transcended the simple mechanics of machines: he discovered a fundamental law governing all energy exchanges in our Universe.
By observing the immutable flow of heat, he brought to light a universal principle which would become the concept entropythis measurement that secretly governs our reality, from subatomic particles to black holes. Two centuries after this fundamental discovery, physicists continue to explore the dizzying ramifications of this notion, revealing unexpected connections between energy, information and consciousness.
Disorder, a law of the Universe
Sadi Carnot, observing the roaring engines of the machines that rumbled in the industrial workshops, understood that heat invariably flowed from hot to cold, never the other way around. This primordial asymmetry hid a deeper truth that Rudolf Clausius formalized in 1865, by introducing the concept of entropy, from the Greek “transformation”. To put it simply, entropy is a measure of the disorder of a systemwhich naturally tends to increase over time.
The real conceptual breakthrough would come later, from Ludwig Boltzmann, an Austrian physicist and philosopher, who revealed the deeply probabilistic nature of entropy in the 1870s. His reasoning is based on a fundamental distinction between two levels of description of the material : the microscopic state, which details the position and speed of each particle, and the macroscopic state, which describes global properties such as temperature or pressure.
For the same macroscopic state, there are a multitude of possible microscopic arrangements. Let’s take the example of a room: the air it contains may have a uniform temperature of 20° C, but the molecules which compose it can be arranged in trillions of different ways while giving this same temperature.
Boltzmann then understands that the entropy of a system is proportional to the logarithm of the number of these possible microscopic configurations. This mathematical approach explains why a gas spontaneously spreads throughout all available space: there are mathematically many more ways for molecules to occupy the entire volume than to remain confined in a corner. Nature does not “prefer” disorder; it simply follows the implacable laws of probability.
This probabilistic approach explains many daily phenomena that we do not pay attention to : why a broken vase never reconstitutes itself, why smoke disperses in the air without ever coming together, why time seems to flow in only one direction. The inexorable increase in entropy inscribes an arrow of time in the laws of physics, transforming it from a simple mathematical coordinate into a lived experience of change.
Time, fruit of our ignorance
It was in the secret laboratories of the Second World War that another discovery would revolutionize our understanding of entropy. Claude Shannon, a young mathematician working on the encryption of military communications, asks himself a seemingly simple question: how to measure the amount of information contained in a message ? Imagine a text where you have to guess each letter. The more predictable the text (like “ Hello Mrs “), the less new information it contains. Conversely, a completely random sequence of characters contains a maximum of information, because each letter is a real surprise.
Shannon developed a mathematical formula to quantify this “informational surprise.” And this is where a stunning coincidence occurs: its equation is strictly identical to that which Boltzmann had established for thermodynamic entropy. This similarity is no coincidence, but reveals a profound truth about the nature of entropy.
Let’s take a simple analogy: faced with a perfectly arranged bookshelf, we can easily describe the position of each book. But if the library is messy, we need a lot more information to describe the exact location of each item. Entropy thus measures our “organized ignorance” of the world.
Physicist Edwin Jaynes took this reasoning even further in the 1950s. When we measure the temperature of a room, we only have access to a rough average of the movement of billions of air molecules. Entropy quantifies our inevitable ignorance of microscopic details. If we observe a forest from an airplane, we can estimate its density, its dominant color, but we cannot distinguish each leaf, each branch or each insect. Entropy represents here the immense amount of information we lose when taking the big picture.
This revolutionary vision unified seemingly unrelated areas. In quantum mechanics, the fundamental impossibility of simultaneously knowing the position and velocity of a particle results in irreducible entropy. A black hole represents the extreme case: all the information about what falls into it becomes inaccessible to the outside observer, creating maximum entropy.
Even our brains, in processing information, generate heat – a direct manifestation of the link between information and energy. Our perception of the passing of time would thus be intimately linked to our inability to know everything and foresee everything.
Two hundred years after Carnot’s work, entropy continues to surprise us. This concept has proven to be a key to understanding the nature of a multitude of other fundamental questions. The inexorable increase in entropy is no longer seen as a cosmic curse, but as the very engine of our existence. In a perfectly ordered universe, no transformation would be possible. It is therefore the growing disorder that allows the emergence of complex structures, from stars to living beings. This disorder also reminds us that we are all ephemeral beings, destined to blend into the great cosmic chaos. So we might as well take advantage of it and live our existence to the fullest. !
- Entropy, born from the reflections of Sadi Carnot, measures the inevitable transition from order to disorder in the universe.
- This concept links probability, information and energy, explaining phenomena as varied as time, black holes or biological systems.
- This universal phenomenon, the key to numerous transformations, is also the engine of complexity and of life itself.
