Where does transition collide?

A phase transition is an abrupt change in the state or bulk properties of a physical system when a control variable such as temperature or pressure crosses a critical point: water freezing to ice, a fluid boiling, or a metal losing its magnetism above a certain temperature. A first-order transition, like melting, absorbs or releases latent heat and holds two phases at once, while a continuous transition, like the loss of magnetism at the Curie point, has no latent heat and shows quantities that diverge near the critical point. Kadanoff and colleagues' 1967 Static Phenomena Near Critical Points set out how these continuous transitions are captured by scaling laws and critical exponents. Here the meaning is a collective change in a material's phase, not a molecule poised at the top of a reaction barrier, a step between states in a random process, or a nation's changing birth and death rates.[1]

Unit

One change of phase in a many-particle system as a control variable crosses its critical value

Recovery means

Many transitions reverse on cooling or compression, though a first-order one can supercool or superheat past the point of change

Measured by

Located by watching a property such as density, magnetisation, or heat capacity jump or diverge as temperature or pressure is scanned

A transition state is the fleeting, highest-energy arrangement of atoms that a set of reacting molecules must pass through on the way from reactants to products: it sits at the very top of the energy barrier along the reaction path, poised between old bonds breaking and new bonds forming. Eyring's 1935 The Activated Complex in Chemical Reactions built transition-state theory around this configuration, treating the rate of a reaction as set by how many molecules reach the peak and how fast they cross it. The meaning here is a single, unstable point on one molecule's journey over a barrier, not a whole material changing phase, a move between states in a random process, or a society's shift in vital rates.[2]

Unit

One highest-energy atomic configuration at the peak of a reaction's energy barrier

Recovery means

Not applicable

Measured by

Inferred from reaction rates and their temperature dependence, and modelled by computing the energy surface between reactants and products

In a stochastic process, a transition is a move from one state to another as the process steps forward in time, and the chance of each possible move is a transition probability. For a Markov chain, where the next state depends only on the present one, these probabilities are gathered into a transition matrix whose rows give the odds of going from a given state to each other state. Norris's 1997 Markov Chains develops the theory around this matrix and how repeated multiplication of it describes the process over many steps. The meaning here is an abstract jump between labelled states in a probability model, not a material changing phase, a molecule crossing a reaction barrier, or a country's changing birth and death rates.[3]

Unit

One step from a present state to a next state, weighted by its transition probability

Recovery means

Not applicable

Measured by

Estimated by counting observed moves between states, or specified in a model as the entries of a transition matrix