# Glossary

Brownian motion
Brownian motion is the seemingly random motion that a small particle (say, a grain of pollen) undergoes when it is suspended in a liquid. First documented by Scottish botanist Robert Brown, it was explained by Einstein as the result of the pollen grain being buffeted by the random motion of molecules in the liquid. Brownian motion is similar to the random walk, and the equations governing Brownian motion can be derived from the random walk equations by making the step size infinitely small along with a few other mathematical assumptions.
catalyze
Some chemical reactions proceed much more quickly in the presence of a particular molecule than they do when that molecule is absent. The molecule, called a "catalyst," is said to catalyze the reaction.
A complex adaptive system, or CAM, is a population of individual components that react to both their environments and to one another. The state of the population is constantly evolving, and emergent behavior often appears. Biological and ecological systems are examples of complex adaptive systems, as are the Internet, human society, and the power grid.
conformation distribution
The internal potential energy that a molecule has depends on its physical structure, or conformation. Molecules tend toward structures that minimize their potential energy. Sometimes there is not a single, unique minimum energy conformation. In this case, the conformation distribution is the set of lowest energy states that a molecule can occupy.
energy landscape
The energy of a physical system can be represented by a mathematical function that depends on several variables. The energy landscape that the system occupies is this function plotted as a hypersurface in space that is one dimension higher than the relevant number of variables. If the energy depends on one variable, then the energy landscape is a line drawn in a two-dimensional plane. If the energy depends on two variables, the energy landscape is a two-dimensional surface embedded in three-dimensional space that can look like mountains and valleys in a real landscape that one might encounter on the Earth's surface. The ground state of a system is the lowest point on the energy landscape.
entropy
Entropy is a quantitative measure of the amount of order in a system. In statistical mechanics, a system's entropy is proportional to the logarithm of the number of states available to the system. If we consider a collection of water molecules, its entropy is greater at room temperature, when the molecules are bouncing around in a gaseous phase, than at very low temperatures, when the molecules are lined up in a rigid crystal structure.
enzymes
Enzymes are proteins that catalyze chemical reactions in biological systems.
fitness landscape
The fitness landscape is a visual representation of how well adapted different genotypes are to a set of environmental conditions. Each possible genotype occupies a point on the landscape. The distance between each pair of genotypes is related to how similar they are, and the height of each point indicates how well adapted that genotype is.
frustrated
A physical system is frustrated if it has no well-defined ground state because there are competing interactions among the pieces of the system that cannot simultaneously be at an energy minimum. A simple example is a system of three spins. If the interaction energy between two spins is lowest when they point in opposite directions, the ground state of a pair of spins is clearly for the two spins to point in opposite directions. If a third spin is added, it is pulled in opposite directions attempting to minimize its interaction with the other two.
genome
An organism's genome is the complete set of genetic information required to reproduce and maintain that organism in a living state.
ground state
The ground state of a physical system is the lowest energy state it can occupy. For example, a hydrogen atom is in its ground state when its electron occupies the lowest available energy level.
handedness
Handedness, also called "chirality," is a directional property that physical systems may exhibit. A system is "right handed" if it twists in the direction in which the fingers of your right hand curl if your thumb is directed along the natural axis defined by the system. Most naturally occurring sugar molecules are right handed. Fundamental particles with spin also exhibit chirality. In this case, the twist is defined by the particle's spin, and the natural axis by the direction in which the particle is moving. Electrons produced in beta-decay are nearly always left handed.
metastable
A metastable state has a higher energy than the ground state that a physical system can become trapped in for some length of time. A simple example is a ball sitting on a hilltop. The ball's energy would be lower if it rolled down the hill; but unless something disturbs it, it will remain where it is. Metastable states of atoms are put to use in atomic clocks because they are long lived, and therefore correspond to a clock frequency that can be known very precisely. In biological physics, valleys in the energy landscape correspond to metastable states, as do low-lying peaks in the fitness landscape.
monomer
A monomer is a small molecule that can bind to other like molecules to form a polymer. The amino acids that make up proteins are examples of monomers.
polar
A polar molecule has a nonzero electric dipole moment, so it has a side that is positively charged and a side that is negatively charged.
polarizability
Some atoms and molecules that have no electric dipole moment in an electrically neutral environment will develop one in an electric field. The polarizability of an atom or molecule is a quantity that describes how susceptible it is to this effect.
polarization
The polarization of a wave is the direction in which it is oscillating. The simplest type of polarization is linear, transverse polarization. Linear means that the wave oscillation is confined along a single axis, and transverse means that the wave is oscillating in a direction perpendicular to its direction of travel. Laser light is most commonly a wave with linear, transverse polarization. If the laser beam travels along the x-axis, its electric field will oscillate either in the y-direction or in the z-direction. Gravitational waves also have transverse polarization, but have a more complicated oscillation pattern than laser light.
polymer
A polymer is a large molecule that is made up of many repeating structural units, typically simple, light molecules, linked together. Proteins are polymers made up of amino acids. See: monomer.
random walk
The random walk is the trajectory that arises when an object moves in steps that are all the same length, but in random directions. The path of a molecule in a gas follows a random walk, with the step size determined by how far (on average) the molecule can travel before it collides with something and changes direction. The behavior of many diverse systems can be modeled as a random walk, including the path of an animal searching for food, fluctuating stock prices, and the diffusion of a drop of food coloring placed in a bowl of water.
Second Law of Thermodynamics
The second law of thermodynamics states that the entropy of an isolated system will either increase or remain the same over time. This is why heat flows from a hot object to a cold object, but not the other way; and why it's easy to dissolve salt in water, but not so easy to get the salt back out again.
Turing machine
In 1937, Alan Turing outlined the details of the Turing machine in a paper investigating the possibilities and limits of machine computation. The machine is an idealized computing device that consists, in its simplest form, of a tape divided up into cells that are processed by an active element called a "head." The cells can be in one of two states. The head moves along the tape, changing the cells from one state to the other and moving either forward or backward according to a set of predetermined instructions. Turing machines can be described with a set of simple mathematical equations that allowed scientists to understand many of the basic properties of digital computing long before the first modern computer was built.