Ludwig BoltzmannLudwig Eduard Boltzmann (ˈluːtvɪç ˈbɔlt͡sman; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy, , where Ω is the number of microstates whose energy equals the system's energy, interpreted as a measure of statistical disorder of a system. Max Planck named the constant kB the Boltzmann constant.
Configuration entropyIn statistical mechanics, configuration entropy is the portion of a system's entropy that is related to discrete representative positions of its constituent particles. For example, it may refer to the number of ways that atoms or molecules pack together in a mixture, alloy or glass, the number of conformations of a molecule, or the number of spin configurations in a magnet. The name might suggest that it relates to all possible configurations or particle positions of a system, excluding the entropy of their velocity or momentum, but that usage rarely occurs.
Invasive speciesAn invasive or alien species is an introduced species to an environment that becomes overpopulated and harms its new environment. Invasive species adversely affect habitats and bioregions, causing ecological, environmental, and/or economic damage. The term can also be used for native species that become harmful to their native environment after human alterations to its food web - for example, the purple sea urchin (Strongylocentrotus purpuratus) which has decimated kelp forests along the northern California coast due to overharvesting of its natural predator, the California sea otter (Enhydra lutris).
Partition function (mathematics)The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution. The partition function occurs in many problems of probability theory because, in situations where there is a natural symmetry, its associated probability measure, the Gibbs measure, has the Markov property.
H-theoremIn classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity H (defined below) in a nearly-ideal gas of molecules. As this quantity H was meant to represent the entropy of thermodynamics, the H-theorem was an early demonstration of the power of statistical mechanics as it claimed to derive the second law of thermodynamics—a statement about fundamentally irreversible processes—from reversible microscopic mechanics.
Introduced speciesAn introduced species, alien species, exotic species, adventive species, immigrant species, foreign species, non-indigenous species, or non-native species is a species living outside its native distributional range, but which has arrived there by human activity, directly or indirectly, and either deliberately or accidentally. Non-native species can have various effects on the local ecosystem. Introduced species that become established and spread beyond the place of introduction are considered naturalized.
Partition function (number theory)In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. No closed-form expression for the partition function is known, but it has both asymptotic expansions that accurately approximate it and recurrence relations by which it can be calculated exactly. It grows as an exponential function of the square root of its argument.
Partition function (quantum field theory)In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism. They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Partition functions can rarely be solved for exactly, although free theories do admit such solutions. Instead, a perturbative approach is usually implemented, this being equivalent to summing over Feynman diagrams.
Endangered speciesAn endangered species is a species that is very likely to become extinct in the near future, either worldwide or in a particular political jurisdiction. Endangered species may be at risk due to factors such as habitat loss, poaching and invasive species. The International Union for Conservation of Nature (IUCN) Red List lists the global conservation status of many species, and various other agencies assess the status of species within particular areas.
Rare speciesA rare species is a group of organisms that are very uncommon, scarce, or infrequently encountered. This designation may be applied to either a plant or animal taxon, and is distinct from the term endangered or threatened. Designation of a rare species may be made by an official body, such as a national government, state, or province. The term more commonly appears without reference to specific criteria. The International Union for Conservation of Nature does not normally make such designations, but may use the term in scientific discussion.
Keystone speciesA keystone species is a species that has a disproportionately large effect on its natural environment relative to its abundance, a concept introduced in 1969 by the zoologist Robert T. Paine. Keystone species play a critical role in maintaining the structure of an ecological community, affecting many other organisms in an ecosystem and helping to determine the types and numbers of various other species in the community. Without keystone species, the ecosystem would be dramatically different or cease to exist altogether.
Entropy (information theory)In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable , which takes values in the alphabet and is distributed according to : where denotes the sum over the variable's possible values. The choice of base for , the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base e gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys".
