Entropy: The physics of disorder


One of the most useful concepts in physics is a property of matter called entropy. It is useful for understanding topics as diverse as how steam engines work to the fate of structure in the universe.

Just as one wouldn’t say an individual atom has a certain temperature or possesses a defined amount of heat, neither would one say it has a specified amount of entropy. Rather these parameters characterize the physical state of conglomerates of atoms and molecules, be they in the form of solids, liquids or gases.

These are emergent macroscopic properties reflecting the collective behavior of all the constituents within a system. While temperature measures the average kinetic energy of all the system’s particles, heat specifies the total amount of kinetic energy possessed by all the particles in the system.

Similarly, entropy quantitates disorder within a system. Saying the entropy of something increases is equivalent to saying the constituents making it up have become more random, chaotic or disordered; the system has lost structure.

Solids are generally composed of parts arranged in a regular structure. This is especially the case with solid crystals where individual atoms are arranged in repeating patterns. Liquids and gases typically are more free-form. Consequently, the entropy of a solid increases as its warmer surroundings cause it to melt and then vaporize.

The strength and nature of mutual attractions between atoms and molecules in solids and liquids accounts for other macroscopic properties as well: hardness, elasticity and tensile strength in solids, viscosity in liquids.

In liquids, atoms or molecules adhere to one another. However their mutual attraction does not constrain them to a rigid structure. Their attraction may cause them to linger in proximity to one another but they eventually drift apart.

Though interactions in liquids are transient, when energy is supplied they can be sufficient to give rise to patterns of collective movement. These include structures such as waves, patterns of flow as in currents, and turbulence as exemplified by eddies.

Though turbulence patterns arise in gases, gases are generally more disordered than liquids. Unless impelled to move collectively in a wind current, the constituents of gases fly about filling the space that confines them. Otherwise, they only interact with one another in random collisions.

The second law of thermodynamics states entropy in a closed system can only stay constant or increase.

The classic illustration of entropy is a block of ice (one sub-system) in a warm room (another sub-system). The room is isolated from everything else, meaning the entire system is closed. Warm air in the room raises the temperature of the ice while slightly dropping the room temperature.

This heat (or energy transfer) continues until the temperature of the room and its contents are equal. The resulting increase in entropy of the melted ice (water) is more than the decrease in entropy of the surrounding room. The net result is an increase in entropy for the entire system; the isolated room and its contents together.

Since the universe doesn’t appear to interact with anything outside its bounds, it is a closed system. As a result, its total entropy will increase and its overall structure will progressively diminish.

If this is so, how does order increase in some parts of the universe such as on the Earth’s surface? Imagine the universe is partitioned into subsystems like the room and block of ice. Order can increase in one subsystem so long as it decreases at least as much somewhere else — robbing Peter to pay Paul, so to speak.

As such, the subsystems are open to each other. Energy emitted by processes of disorder in one location is absorbed by processes creating order somewhere else. Taken together, the “somewhere else” and the place becoming more disordered, there must be a net increase in entropy.

So long as entropy in the entire composite system increases, the second law doesn’t prohibit one region from gaining order at the expense of another.

Let’s assume our solar system is isolated (which, strictly speaking, it is not). The entropy of the sun increases as it burns. By emitting large amounts of energy it becomes cooler. Consequently, it loses structure, becoming progressively less dynamic.

Much of the order on Earth’s surface is attributable to interactions with the sun. Absorption of energy from sunlight drives mechanisms that create many structures. These include atmospheric winds, ocean currents and ultimately all organisms. Earthly structures of this sort are made possible by the sacrifice of structure on the sun.

Of course our planet only absorbs a small fraction of the sun’s radiant energy; the rest is lost to interstellar space. The sun will eventually burn out. The entropy of the larger “closed” sun-Earth system will continue to increase and structure will be progressively lost.

Simple things like crystals have a regular structure, meaning their descriptions are compact. That is, they can be characterized by a relatively small amount of information; take the local pattern and repeat it. Complex structures require more information, which only increases when their structure disintegrates.

This leads to the idea that there is a kind of equivalence between entropy and information. That is, as entropy increases, the resulting less structured state of matter requires more information for its characterization.

The concept of entropy arose to explain the operation of steam engines. Now, at the cutting edge of cosmology, Stephen Hawking asks what happens to the information (entropy) associated with structures in interstellar space when they are gobbled up by black holes.

Physics deals with fundamental, universal truths about the workings of the physical universe. What could be more universal than ideas that relate to both steam engines and black holes?

Steve Luckstead is a medical physicist in the radiation oncology department at St. Mary Medical Center. He can be reached at steveluckstead@charter.net.


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