In
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
, the metastate is a
probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as ''countable additivity''. The difference between a probability measure and the more ge ...
on the
space of all thermodynamic states for a system with quenched randomness. The term metastate, in this context, was first used in by
Charles M. Newman and
Daniel L. Stein in 1996..
Two different versions have been proposed:
1) The
Aizenman-Wehr construction, a
canonical ensemble
In statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. The system can exchange energy with the heat b ...
approach,
constructs the metastate through an ensemble of states obtained by varying
the random parameters in the
Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
outside of the volume being
considered.
2) The
Newman
Newman is a surname of English origin and may refer to many people:
The surname Newman is widespread in the core Anglosphere.
A
*Abram Newman (1736–1799), British grocer
* Adrian Newman (disambiguation), multiple people
* Al Newman (born 196 ...
-
Stein
Stein is a German, Yiddish and Norwegian word meaning "stone" and "pip" or "kernel". It stems from the same Germanic root as the English word stone. It may refer to:
Places In Austria
* Stein, a neighbourhood of Krems an der Donau, Lower Aus ...
metastate, a
microcanonical ensemble approach,
constructs an empirical average from a deterministic (i.e., chosen
independently of the randomness) subsequence of finite-volume
Gibbs distributions.
It was proved
for Euclidean lattices that there always
exists a deterministic subsequence along which the Newman-Stein and
Aizenman-Wehr constructions result in the same metastate. The metastate is
especially useful in systems where deterministic sequences of volumes fail
to converge to a
thermodynamic state
In thermodynamics, a thermodynamic state of a system is its condition at a specific time; that is, fully identified by values of a suitable set of parameters known as state variables, state parameters or thermodynamic variables. Once such a set ...
, and/or there are many competing
observable thermodynamic states.
As an alternative usage, "metastate" can refer to
thermodynamic states, where the system is in a
metastable state
In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy.
A ball resting in a hollow on a slope is a simple example of metastability. If the ball i ...
(for example
superheated or undercooled liquids, when the actual temperature of the liquid is above or below the boiling or freezing temperature, but the material is still in a liquid state).
[Debenedetti, P.G.Metastable Liquids: Concepts and Principles; Princeton University Press: Princeton, NJ, USA, 1996.][{{cite journal , last1=Imre , first1=Attila , last2=Wojciechowski , first2=Krzysztof , last3=Györke , first3=Gábor , last4=Groniewsky , first4=Axel , last5=Narojczyk , first5=Jakub. , title=Pressure-Volume Work for Metastable Liquid and Solid at Zero Pressure , journal=Entropy , publisher=MDPI AG , volume=20 , issue=5 , date=3 May 2018 , issn=1099-4300 , doi=10.3390/e20050338 , page=338, pmid=33265428 , pmc=7512857 , bibcode=2018Entrp..20..338I , doi-access=free]
References
Statistical mechanics
Condensed matter physics