The Laws of Thermodynamics PART 4

The Laws of Thermodynamics PART 1 click here
The Laws of Thermodynamics PART 2 click here
The Laws of Thermodynamics PART 3 click here

The Third Law of Thermodynamics

The last in this four-part series of articles explores the third law, which focuses on the properties of  systems that approach absolute zero. The eerie quantum behaviour of matter becomes observable in extremely cold systems. At much warmer temperatures, molecules and atoms have so much kinetic energy they cannot form the chemical bonds that hold liquids or solids together. However, as absolute zero approaches, such random particle motion is quieted down enough to begin to reveal matter's underlying quantum nature. A tremendous amount of research is underway to explore how how ultra cold matter behaves. New and exotic behaviours, such as superfluidity, emerge as the system's thermal energy approaches zero. The third thermodynamic law is all about the energy of matter as it approaches absolute zero.

This law can be stated a few different ways. Put most simply, the entropy of a pure substance approaches zero when its temperature approaches absolute zero (0 K, -273.15°C, -459.67°F). It is a statement about the limits of temperature and entropy in a system. What is absolute zero? A substance, if it could reach exactly 0 K, would have no thermal energy left at all. Although it is theoretically possible, 0 K doesn't exist in nature, and this law really explores the reason why that is so. The coldest measured object in the universe is the Boomerang Nebula, which contains gases cooled to just 1 K. These gases are even colder than the empty space around them and that initially presented a puzzle. Background microwave radiation warms empty space to 2.73 K, so how is it possible to cool an object down more than the space around it? This posed a mystery to scientists until recently. They think that the Boomerang Nebula was created when a dying red giant star exploded as a smaller-mass companion star crashed into it, creating an exceptionally powerful explosion that ejected stellar gases outward at such velocity (10 times faster than a single exploding red giant of comparable mass) that the gas adiabatically expanded into an ultra-cold gas. The gas cloud would then gradually absorb heat from the microwave radiation bathing the space it occupies, until it reaches equilibrium with it, at 2.73 K

As matter approaches 0 K, atoms lose thermal energy. The electrons in atoms eventually fall down into low energy states. Does zero thermal energy mean that a system has zero entropy as well? Not necessarily, and this is the key point. When many substances freeze, they settle into a three-dimensional lattice-like arrangement. Crystallography is the science that explores those arrangements that atoms assume when a substance freezes into a crystal. Only a perfect crystal of a pure substance could actually reach absolute zero. Only in such a flawless atomic arrangement could atoms lock into such a perfect alignment that has zero thermal energy. Atoms in it would not have any kinetic energy. They would not move about slightly in the lattice or undergo any translational or rotational movements. Even at 0 K, however, each atom would still vibrate (in its lowest energy state) about its equilibrium position within the crystal, but this motion is not transferable as heat. Individual molecules and atoms can never be totally frozen. They are quantum clouds that are always in motion associated with the uncertainty principle, and electrons by their nature are never stationary. None of this motion is thermal motion.

A perfect crystal would have to contain only one kind of atom or molecule. Otherwise there would be entropy associated with the mixing of two or more microstates (you can also say there is more than one microscopic configuration possible). We are reminded that entropy is also about the multiplicity of possible states in a system.

A perfect crystal, though impossible to create, is useful because it offers a benchmark we can use to describe what happens to entropy as real substances are cooled to absolute zero. Microscopic imperfections always form when substances crystallize, no matter how controlled the procedure is. Any imperfection in a crystal lattice adds disorder and therefore entropy. Even the most flawless diamond, for example, is never perfect. Defects inevitably get frozen into a crystal that pull the lattice pattern out of alignment. If just a single boron atom replaces a carbon atom in a diamond crystal, for example, it will shift the whole alignment microscopically, reducing the microscopic order and increasing its entropy. All pure substances that in theory would condense into perfect crystals have, in reality, point defects. Such a defect could be a single replacement (like boron for carbon) or a hole created by a missing atom. It could be a linear defect or a planar defect. These are all called crystallographic defects. Every crystallographic defect adds residual entropy to a crystal, and would prevent it from ever reaching 0 K.

Some pure substances, even if they could be entirely defect-free, will still never settle into an absolutely perfect lattice formation. These substances cannot reach 0 K because of their atomic makeup. They will always retain a certain amount of residual entropy. A classic example is carbon monoxide (CO). A CO molecule has a small dipole moment, which means it has a slightly lopsided charge (it has "a left" and "a right"). When the gas is cooled down far enough it will eventually form crystals. Those crystals will not be perfect because each CO molecule can be oriented CO or OC. The dipole moment is too small to assure that all align in one direction so there is a chance that CO could crystallize in another pattern such as CO:OC:CO instead of CO:CO:CO, for example. We can estimate this contribution to the crystal's entropy by calculating how many possible microstates a crystal sample of a certain number of molecules can achieve. For carbon monoxide we know there are two ways each CO molecule can exist in the lattice so we can give a value w = 2. For an N number of CO molecules in the crystal, there are wN ways, or 2N ways in this case, that the CO molecules can be arranged. There are 2N different microstates possible, and entropy, we now know, is all about the number of possible states a system can be in.

When carbon monoxide freezes into a crystal, it becomes locked into one of many possible ground states, each of which corresponds to a specific microscopic configuration. It therefore must have residual entropy even at 0 K. Put more scientifically, carbon monoxide has a degenerate, or asymmetrical, ground state. Asymmetrical ground states are very interesting to study. Times crystals, mentioned earlier, show that an asymmetrical ground state can be one in space (as with the carbon monoxide crystal) or one in time and space (as in a time crystal). These crystals have a very unusual property. While ordinary crystals, such as carbon monoxide, have an atomic structure that repeats in space, time crystals repeat in time as well: they maintain a constant perfectly regular atomic-level oscillation while in their ground energy state. Researchers thought this was impossible - the atoms in substances at ground state should be locked in place and shouldn't change because there is no energy available to change. Yet a time crystal changes from moment to moment, leading researchers to wonder if it is doing work without any input of energy, a microscopic sort of perpetual motion machine that (gasp!) breaks the second law of thermodynamics.

Technically a time crystal is indeed a system with no thermal energy available to do work. It was also assumed to be an isolated system, where no thermal energy is transferred into the system. Upon close study, however, physicists discovered that a time crystal system is not closed. Even though it is in its ground state and remains in its ground state, it is actually an open non-equilibrium system (and the first non-equilibrium ground state system ever discovered).

Proposed theoretically in 2012, time crystals were recently created in the lab. One way to create a time crystal is to line up a set of ytterbium atoms, all of which have quantum-entangled electrons, that is laser-cooled to its ground state. Then it is deliberately kept out of equilibrium by hitting the atoms with two alternating lasers. It is open to the environment and energy is continuously being supplied to the crystal. If the lasers are turned off the crystal stops oscillating. The fine point here is that it's not a transfer of thermal energy because the atoms stay in ground state. If even very slight changes were made to the magnetic field or to the laser pulses, the ytterbium line "melted," changing its phase of matter, a clear signal that thermal energy was absorbed by the atoms. The time crystal therefore does not convert thermal energy into mechanical work. To make the time crystal "tick," one laser sets up a magnetic field that the electrons respond to and the other one flips the spins of some of the atoms. All the atoms are entangled so they all settle into a perfectly stable repetitive spin-flipping pattern that, strangely, is exactly half the rate of the laser pulses. There is no heat exchange or change in entropy because it is in only one ground state at a time. Rather than being a thermodynamic process, this motion, without thermal or kinetic energy, appears to be the first example of broken time translation symmetry observed in nature. Time translation symmetry is the fundamental assertion that the laws of physics don't change over time, and the conservation of energy in nature depends on it. Scientists make the distinction that if time symmetry is broken explicitly, then the laws of nature can no longer be counted on. In a time crystal, however, the symmetry is broken spontaneously, which means that, only in a specific case, nature chooses a state that doesn't obey time translation symmetry. This exception to the rule is analogous to the breaking of CP and time symmetry observed by the weak force mentioned earlier.

Conclusion

The laws of thermodynamics have an all-encompassing scope. They preside over every other science from biology, to geology, chemistry, astrophysics and quantum physics, to name just a few. They outline the basic rules that every process within the vast universe to the sub-atomic realm must follow, which means that these rules must work to explain the extremes of nature, such as black holes. Every scientific discipline from engineering to the applied chemistries to quantum computing must take thermodynamics into account when systems are designed. The laws can also be harnessed as a tool to probe into the mysteries of space-time and quantum behaviour.

Thermodynamics impacts us all personally. It underlies everything we do in life. It is essential to understanding how all life processes work, and how life evolved on this planet. It will be an essential component in our search for efficient energy sources of the future. It will even help us look for and recognize life on other worlds, as scientists imagine all the ways living systems could utilize exotic sources of energy. Anytime energy is converted from one form into another, or into work and vice versa, in any process, thermodynamics determines what can happen and what can't happen and why.