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E


   
Effective mass In a vibrating system, a particular vibrational mode can be described as a harmonic oscillator with some mass and stiffness. Given some measure of vibrational amplitude, there exists a unique choice of mass and stiffness that yields the correct values for both frequency and energy; these are the effective mass and effective stiffness.
   
Effective stiffness See effective mass.
   
Elastic An object behaves elastically if it returns to its original shape after a force is applied and then removed. (If an applied force causes a permanent deformation, the behavior is termed plastic.) In an elastic system, the internal potential energy is a function of shape alone, independent of past forces and deformations.
   
Electron density The location of an electron is not fixed, but is instead described by a probability density function. The sum of the probability densities of all the electrons in a region is the electron density in that region.
   
Electronegativity A measure of the tendency of an atom (or moiety) to withdraw electrons from structures to which it is bonded. In most circumstances, for example, sodium tends to donate electron density (it has a low electronegativity) and fluorine tends to withdraw electron density (it has a high electronegativity).
   
Electronic Pertaining to the energies, distributions, and behaviors of electrons; see mechanical.
   
Endoergic A transformation is termed endoergic if it absorbs energy; such a reaction increases molecular potential energy. (Sometimes wrongly equated to the narrower term endothermic.)
   
Endothermic A transformation is termed endothermic if it absorbs energy in the form of heat. A typical endothermic reaction increases both entropy and molecular potential energy (and is thus analogous to a gas expanding while absorbing heat and compressing a spring).
   
Energy A conserved quantity that can be interconverted among many forms, including kinetic energy, potential energy, and electromagnetic energy. Sometimes defined as "the capacity to do work,'' but in an environment at a uniform nonzero temperature, thermal energy does not provide this capacity. (Note, however, that all energy has mass, and thus can be used to do work by virtue of its gravitational potential energy; this caveat, however, is of no practical significance unless a really deep gravity well is available.) See free energy.
   
Enthalpy The enthalpy of a system is its actual energy (termed the internal energy) plus the product of its volume and the external pressure. Though sometimes termed "heat content,'' the enthalpy in fact includes energy not contained in the system. Enthalpy proves convenient for describing processes in gases and liquids in laboratory environments, if one does not wish to account explicitly for energy stored in the atmosphere by work done when a system expands. It is of little use, however, in describing processes in nanomechanical systems, where work can take many forms: internal energy is then more convenient. Enthalpy is to energy what the Gibbs free energy is to the Helmholtz free energy.
   
Entropy A measure of uncertainty regarding the state of a system: for example, a gas molecule at an unknown location in a large volume has a higher entropy than one known to be confined to a smaller volume. Free energy can be extracted in converting a low-entropy state to a high-entropy state: the (time-average) pressure exerted by a gas molecule can do useful work as a small volume is expanded to a larger volume. In the classical configuration space picture, any molecular system can be viewed as a single-particle gas in a high-dimensional space. In the quantum mechanical picture, entropy is described as a function of the probabilities of occupancy of different members of a set of alternative quantum states. Increased information regarding the state of a system reduces its entropy and thereby increases its free energy, as shown by the resulting ability to extract more work from it.
An illustrative contradiction in the simple textbook view of entropy as a local property of a material (defining an entropy per mole, and so forth) can be shown as follows: The third law of thermodynamics states that a perfect crystal at absolute zero has zero entropy*; this is true regardless of its size. A piece of disordered material, such as a glass, has some finite entropy G0 > 0 at absolute zero. In the local-property view, N pieces of glass, even (or especially) if all are atomically identical, must have an entropy of NG0. If these N pieces of glass are arranged in a regular three-dimensional lattice, however, the resulting structure constitutes a perfect crystal (with a large unit cell); at absolute zero, the third law states that this crystal has zero entropy, not NG0. To understand the informational perspective on entropy, it is a useful exercise to consider (1) what the actual entropy of such crystal is as a function of N, with and without information describing the structure of the unit cell, (2) how the third law can be phrased more precisely, and (3) what this more precise statement implies for the entropy of well-defined aperiodic structures. Note that any one unit cell in the crystal can be regarded as a description of all the rest.
   
Enzyme A protein molecule that acts as a specific catalyst, binding to other molecules in a manner that facilitates a particular chemical reaction.
   
Equilibrium A system is said to be at equilibrium (with respect to some set of feasible transformations) if it has minimal free energy. A system containing objects at different temperatures is in disequilibrium, because heat flow can reduce the free energy. Springs have equilibrium lengths, reactants and products in solution have equilibrium concentrations, thermally excited systems have equilibrium probabilities of occupying various states, and so forth.
   
Ester A molecule containing an ester linkage, a carbonyl group bonded to an O that is in turn bonded to a C.
   
Ether A molecule containing a C-O-H double bond to another O, making this part of an ester linkage, or some other exception holds).
   
Eutactic Characterized by precise molecular order, like that of a perfect crystal, the interior of a protein molecule, or a machine-phase system; contrasted to the disorder of bulk materials, solution environments, or biological structures on a cellular scale. Borderline cases can be identified, but perfection is not necessary. As a crystal with sparse defects is best described as a crystal (rather than as amorphous), so a eutactic structure with sparse defects is best described as (imperfectly) eutactic, rather than as disordered.
   
Excluded volume The presence of one molecule (or moiety) reduces the volume available for other molecules (or moieties); resulting reductions in their entropy are termed excluded volume effects.
   
Exoergic The opposite of endoergic; describes a transformation that releases energy.
   
Exothermic The opposite of endothermic; describes an exoergic transformation in which energy is released as heat. Exoergic reactions in solution are commonly exothermic.
 
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* Some textbooks state a slightly weaker form: a reaction that converts perfect crystals at absolute zero into other perfect crystals at absolute zero results in no change in entropy. This is essentially equivalent.

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