A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events.
Chain reactions are one way in which systems which are in thermodynamic non-equilibrium can release energy or increase entropy in order to reach a state of higher entropy. For example, a system may not be able to reach a lower energy state by releasing energy into the environment, because it is hindered in some way from taking the path that will result in the energy release. If a reaction results in a small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released. Since chain reactions result in energy transformation into forms associated with larger amounts of entropy. In accordance with the laws of thermodynamics, the reactions cannot be reversed.
A macrosopic metaphor for chain reactions is thus a snowball causing larger snowfall until finally an avalanche results ("snowball effect"). This is a result of stored gravitational potential energy seeking a path of release over friction. Chemically, the equivalent to a snow avalanche is a spark causing a forest fire. In nuclear physics, a single stray neutron can result in an prompt critical event, which may be finally be energetic enough for a nuclear reactor meltdown or (in a bomb) a nuclear explosion.
Chemical chain reactions 
In 1913 the German chemist Max Bodenstein first put forth the idea of chemical chain reactions. If two molecules react, not only molecules of the final reaction products are formed, but also some unstable molecules, having the property of being able to further react with the parent molecules with a far larger probability than the initial reactants. In the new reaction, further unstable molecules are formed besides the stable products, and so on.
In 1923, Danish and Dutch scientists Christian Christiansen and Hendrik Anthony Kramers, in an analysis of formation of polymers, pointed out that such a chain reaction need not start with a molecule excited by light, but could also start with two molecules colliding violently in the traditional way classically previously proposed for initiation of chemical reactions, by van' t Hoff.
Christiansen and Kramers also noted that if, in one link of the reaction chain, two or more unstable molecules are produced, the reaction chain would branch and grow. The result is in fact an exponential growth, thus giving rise to explosive increases in reaction rates, and indeed to chemical explosions themselves. This was the first proposal for the mechanism of chemical explosions.
A quantitative chain chemical reaction theory was created by Soviet physicist Nikolay Semyonov in 1934. Semyonov shared the Nobel Prize in 1956 with Sir Cyril Norman Hinshelwood, who independently developed many of the same quantitative concepts.
The main steps of chain reaction are the following.
- Initiation (at this step an active particle, often a free radical, is produced);
- propagation (may comprise several elementary steps, as, for instance, reaction elementary acts, where the active particle through reaction forms another active particle which continues the reaction chain by entering the next elementary step); particular cases are:
- * chain branching (the case of propagation step when more new active particles form in the step than enter it);
- * chain transfer (the case in which one active particle enters an elementary reaction with the inactive particle which as a result becomes another active particle along with forming of another inactive particle from the initial active one);
- termination (elementary step in which active particle loses its activity without transferring the chain; e. g. recombination of the free radicals).
The reaction H2 + Br2 → 2 HBr proceeds by the following mechanism:
- Br2 → 2 Br•
- each Br atom is a free radical, indicated by the symbol « • » representing an unpaired electron;
- Propagation (here a cycle of two steps)
- Br• + H2 → HBr + H•
- H• + Br2 → HBr + Br•
- the sum of these two steps corresponds to the overall reaction H2 + Br2 → 2 HBr, with catalysis by Br• which participates in the first step;
- Retardation (inhibition)
- H• + HBr → H2 + Br•
- this step is specific to this example, and corresponds to the first propagation step in reverse;
- termination 2 Br• → Br2
- recombination of two radicals, corresponding in this example to initiation in reverse.
Nuclear chain reactions 
A nuclear chain reaction was proposed by Leó Szilárd in 1933, shortly after the neutron was discovered, but more than five years before nuclear fission was discovered. Szilárd knew of chemical chain reactions, and he had been reading about an energy-producing nuclear reaction involving high-energy protons bombarding lithium, demonstrated by John Cockcroft and Ernest Walton, in 1932. Now, Szilárd proposed to use neutrons theoretically-produced from certain nuclear reactions in lighter isotopes, to induce further reactions in light isotopes that produced more neutrons. This would in theory produce a chain reaction at the level of the nucleus. He did not envision nuclear fission as one of these neutron-producing reactions, since this reaction was not known at the time. Experiments he proposed using beryllium and indium failed.
Later, after nuclear fission was discovered in 1938, Szilárd immediately realized the possibility of using neutron-induced fission as the particular nuclear reaction needed for a chain-reaction, so long as fission also produced neutrons. In 1939, with Enrico Fermi, Szilárd proved this neutron-multiplying reaction in uranium. In this reaction, a neutron plus a fissionable atom causes a fission resulting in a larger number of neutrons than the single one that was consumed in the initial reaction. Thus was born the practical nuclear chain reaction by the mechanism of neutron-induced nuclear fission.
Specifically, if one or more of the produced neutrons themselves interact with other fissionable nuclei, and these also undergo fission, then there is a possibility that the macroscopic overall fission reaction will not stop, but continue throughout the reaction material. This is then a self-propagating and thus self-sustaining chain reaction. This is the principle for nuclear reactors and atomic bombs.
Demonstration of a self-sustaining nuclear chain reaction was accomplished by Enrico Fermi and others, in the successful operation of Chicago Pile-1, the first artificial nuclear reactor, in late 1942.
Electron avalanche in gases 
An electron avalanche happens between two unconnected electrodes in a gas when an electric field exceeds a certain theshold. Random thermal collisions of gas atoms may result in a few free electrons and positively-charged gas ions, in a process called impact ionizaton. Acceleration of these free electrons in a strong electric field causes them to gain energy, and when they impact other atoms, the energy causes release of new free electrons and ions (ionization), which fuels the same process. If this process happens faster than it is naturally quenched by ions recombining, the new ions multiply in successive cycles until the gas breaks down into a plasma and current flows freely in a discharge.
Electron avalanches are essential to the dielectric breakdown process within gases. The process can culminate in corona discharges, streamers, leaders, or in a spark or continuous electric arc that completely bridges the gap. The process may extends to huge sparks — streamers in lightning discharges propagate by formation of electron avalanches created in the high potential gradient ahead of the streamers' advancing tips. Once begun, avalanches are often intensified by the creation of photoelectrons as a result of ultraviolet radiation emitted by the excited medium's atoms in the aft-tip region. The extremely high temperature of the resulting plasma cracks the surrounding gas molecules and the free ions recombine to create new chemical compounds.
The process can also be used to detect radiation that initiates the process, as the passage of a single particles can amplified to large discharges. This is the mechanism of a Geiger counter and also the visualization possible with a spark chamber and other wire chambers.
Avalanche breakdown in semiconductors 
An avalanche breakdown process can happen in semiconductors, which in some ways conduct electricity analogously to a mildly-ionized gas. Semiconductors rely on free electrons knocked out of the crystal by thermal vibration for conduction. Thus, unlike metals, semiconductors become better conductors the higher the temperature. This sets up conditions for the same type of positive feedback—heat from current flow causes temperature to rise, which increases charge carriers, lowering resistance, and causing more current to flow. This can continue to the point of complete breakdown of normal resistance at a semiconductor junction, and failure of the device (this may be temporary or permanent depending on whether there is physical damage to the crystal). Certain devices, such as avalanche diodes, deliberately make use of the effect.
Chain Reactions in Economics 
In 1963 Friedman and Schwartz  proposed a positive feedback loop as a mechanism for catastrophic failures in economics: “It happens that a liquidity crisis in a unit fractional reserve banking system is precisely the kind of event that trigger- and often has triggered- a chain reaction. And economic collapse often has the character of a cumulative process. Let it go beyond a certain point, and it will tend for a time to gain strength from its own development as its effects spread and return to intensify the process of collapse”.
Further examples 
- In a chemical reaction, every step of H2 + Cl2 chain reaction consumes one molecule of H2 or Cl2, one free radical H· or Cl· producing one HCl molecule and another free radical.
- Polymerase chain reaction, a technique used in molecular biology to amplify (make many copies of) a piece of DNA by in vitro enzymatic replication using a DNA polymerase.
See also 
- Cascading failure, a failure in a system of interconnected parts, for example a power transmission grid, where the service provided depends on the operation of a preceding part, and the failure of a preceding part can trigger the failure of successive parts.
- Multiple-vehicle collision
- http://nobelprize.org/nobel_prizes/chemistry/laureates/1956/press.html History of the chemical chain reaction from 1913 to the Nobel work recognized in 1956
- P. Atkins and J. de Paula Physical Chemistry (8th ed., W.H. Freeman 2006), p.831
- "Lab Note #106 Environmental Impact of Arc Suppression". Arc Suppression Technologies. April 2011. Retrieved March 15, 2012.
- Friedman and Schwartz 1963: P.419: The Banking Crisis in USA: