# Microstate

A microstate or ministate is a sovereign state having a very small population or very small land area, and usually both. The meanings of "state" and "very small" are not well-defined in international law.[1] Recent attempts, since 2010, to define microstates have focused on identifying political entities with unique qualitative features linked to their geographic or demographic limitations. According to a qualitative definition, microstates are: "modern protected states, i.e. sovereign states that have been able to unilaterally depute certain attributes of sovereignty to larger powers in exchange for benign protection of their political and economic viability against their geographic or demographic constraints."[2] In line with this and most other definitions, examples of microstates include Liechtenstein, Monaco, San Marino, Andorra, the Cook Islands, Niue, and the Federated States of Micronesia.

The smallest political unit recognized as a sovereign state is Vatican City, with 842 citizens as of July 2013 and an area of only 44 hectares (110 acres). However, some scholars dispute qualifying the Vatican as a state, arguing that it does not meet the "traditional criteria of statehood" and that the "special status of the Vatican City is probably best regarded as a means of ensuring that the Pope can freely exercise his spiritual functions, and in this respect is loosely analogous to that of the headquarters of international organisations."[3]

Microstates are distinct from micronations, which are not recognized as sovereign states. Special territories without full sovereignty, such as the British Crown Dependencies, the Chinese Special Administrative Regions and overseas territories of Denmark, France, the Netherlands, Australia, Norway, the United States and the United Kingdom, are also not considered microstates.

The world's five smallest sovereign states by area, from largest to smallest: San Marino, Tuvalu, Nauru, Monaco, and Vatican City shown in the same scale for size comparison.
Map of the smallest states in the world by land area. Note many of these are not considered microstates.

## Quantitative definitions of microstates and their limitations

Most scholars identify microstates by using a quantitative threshold and applying it to either one variable (such as the size of its territory[4] or population[5]) or a composite of different variables.[6] While it is agreed that microstates are the smallest of all states, there is no consensus on what variable (or variables) or what cut-off point should be used to determine which political units should be labelled as "microstates" (as opposed to small "normal" states).[1][2][7][8]

Map of European ministates; Liechtenstein, San Marino, Malta, Monaco, Vatican and Andorra

### By area

Sovereign states with a non-sea area less than 1,000 km2 (386 sq mi)[9][10] [11][12]
Rank Country / Territory Area (km²/sqmi) Capital city Region
1   Vatican City 0.44 km2 (0.17 sq mi) Vatican City Europe
2  Monaco 2.02 km2 (0.78 sq mi) Monaco-Ville Europe
3  Nauru 21 km2 (8 sq mi) Yaren Oceania
4  Tuvalu 26 km2 (10 sq mi) Funafuti Oceania
5  San Marino 61 km2 (24 sq mi) San Marino Europe
6  Liechtenstein 160 km2 (62 sq mi) Vaduz Europe
7  Marshall Islands 181 km2 (70 sq mi) Majuro Oceania
8  Saint Kitts and Nevis 261 km2 (101 sq mi) Basseterre Caribbean
9  Maldives 298 km2 (115 sq mi) Malé AsiaIndian Ocean
10  Malta 316 km2 (122 sq mi) Valletta EuropeMediterranean Sea
11  Grenada 344 km2 (133 sq mi) St. George's Caribbean
12  Saint Vincent and the Grenadines 389 km2 (150 sq mi) Kingstown Caribbean
13  Barbados 430 km2 (166 sq mi) Bridgetown Caribbean
14  Antigua and Barbuda 443 km2 (171 sq mi) St. John's Caribbean
15  Seychelles 455 km2 (176 sq mi) Victoria AfricaIndian Ocean
16  Palau 459 km2 (177 sq mi) Ngerulmud Oceania
17  Andorra 468 km2 (181 sq mi) Andorra la Vella Europe
18  Saint Lucia 616 km2 (238 sq mi) Castries Caribbean
19  Micronesia, Federated States of 702 km2 (271 sq mi) Palikir Oceania
20  Singapore 714 km2 (276 sq mi) Singapore Asia
21  Tonga 747 km2 (288 sq mi) Nukuʻalofa Oceania
22  Dominica 751 km2 (290 sq mi) Roseau Caribbean
23  Bahrain 765 km2 (295 sq mi) Manama AsiaPersian Gulf
24  Kiribati 811 km2 (313 sq mi) Tarawa Oceania
25  São Tomé and Príncipe 964 km2 (372 sq mi) São Tomé AfricaAtlantic Ocean
With the exceptions of Singapore and Bahrain, all the above have fewer than 500,000 people.

### By population

Sovereign states with fewer than 500,000 people by latest national statistics or CIA Factbook estimate 2014.[9]
Rank Country/territory/entity Population Density (pop./km²) Capital Region
1   Vatican City 842 1913.6 Vatican City Europe
2  Nauru 9,488 451.8 Yaren Oceania
3  Tuvalu 10,782 414.7 Funafuti Oceania
4  Palau 21,186 46.2 Ngerulmud Oceania
5  San Marino 32,742 536.8 San Marino Europe
6  Monaco 37,308 18469.3 Monaco-Ville Europe
7  Liechtenstein 37,313 233.2 Vaduz Europe
8  Saint Kitts and Nevis 51,538 197.5 Basseterre Caribbean
9  Marshall Islands 70,983 392.2 Majuro Oceania
10  Dominica 73,449 97.8 Roseau Caribbean
11  Andorra 85,458 182.6 Andorra la Vella Europe
12  Antigua and Barbuda 91,295 206.1 St. John's Caribbean
13  Seychelles 91,650 201.4 Victoria Africa - Indian Ocean
14  Saint Vincent and the Grenadines 102,918 264.6 Kingstown Caribbean
15  Kiribati 104,488 128.8 Tarawa Oceania
16  Micronesia, Federated States of 105,681 150.5 Palikir Oceania
17  Tonga 106,440 142.5 Nukuʻalofa Oceania
18  Grenada 110,152 320.2 St. George's Caribbean
19  Saint Lucia 163,362 265.2 Castries Caribbean
20  São Tomé and Príncipe 190,428 197.5 São Tomé Africa - Atlantic Ocean
21  Samoa 196,628 69.5 Apia Oceania
22  Vanuatu 266,937 21.9 Port Vila Oceania
23  Barbados 289,680 673.7 Bridgetown Caribbean
24  Iceland 317,351 3.1 Reykjavík Europe
25  Bahamas 321,834 23.2 Nassau Atlantic Ocean
26  Belize 340,844 14.8 Belmopan North America
27  Maldives 393,595 1320.8 Malé Asia - Indian Ocean
28  Malta 412,655 1305.9 Valletta Europe - Mediterranean Sea
29  Brunei 422,675 73.3 Bandar Seri Begawan Asia
With the exceptions of Samoa, Vanuatu, Iceland, Bahamas, Belize, and Brunei, all the above have a non-sea area less than 1,000 km2 (386 sq mi).

While employing simple quantitative criteria may seem straightforward, it can also be perceived as potentially problematic. According to some scholars the quantitative approach to defining microstates suffers from such problems as "inconsistency, arbitrariness, vagueness and inability to meaningfully isolate qualitatively distinct political units"[2]

## Qualitative definitions

In response to the problems associated with the quantitative definitions of microstates, some academics have suggested finding states with unique features linked to their geographic or demographic smallness.[2][10][13] Newer approaches have proposed looking at the behaviour or capacity to operate in the international arena in order to determine which states should deserve the microstate label.[13][14] Yet, it has been argued that such approaches could lead to either confusing microstates with weak states[7][10] (or failed states) or relying too much on subjective perceptions.[2]

### Microstates as modern protected states

In order to address both the problems with quantitative approaches and with definitions based on qualitative features, it has been argued that a useful and meaningful way to isolate microstates from other types of states, would be to see them as "modern protected states".[2] According to the definition proposed by Dumienski (2014): "microstates are modern protected states, i.e. sovereign states that have been able to unilaterally depute certain attributes of sovereignty to larger powers in exchange for benign protection of their political and economic viability against their geographic or demographic constraints."[2] Adopting this approach permits limiting the number of microstates and separating them from both small states and autonomies or dependencies.[2] Examples of microstates understood as modern protected states include such states as: Liechtenstein, San Marino, Monaco, Niue, Andorra, the Cook Islands or Palau.

## Historical anomalies and aspirant states

A small number of tiny sovereign political units are founded on historical anomalies or eccentric interpretations of law. These types of states, often labelled as "microstates," are usually located on small (usually disputed) territorial enclaves, generate limited economic activity founded on tourism and philatelic and numismatic sales, and are tolerated or ignored by the nations from which they claim to have seceded.

One example is the Republic of Indian Stream, now the town of Pittsburg, New Hampshire—a geographic anomaly left unresolved by the Treaty of Paris that ended the U.S. Revolutionary War, and claimed by both the U.S. and Canada. Between 1832 and 1835, the area's residents refused to acknowledge either claimant.

Another example is the Cospaia Republic, which became independent through a treaty error and survived from 1440 to 1826. Its independence made it important in the introduction of tobacco cultivation to Italy.

Another is Couto Misto, disputed by Spain and Portugal, that operated as a sovereign state in its own right until the 1864 Treaty of Lisbon that partitioned the territory, with the largest part becoming part of Spain.

## References

1. ^ a b Warrington, E. (1994). "Lilliputs Revisited". Asian Journal of Public Administration, 16(1).
2. Dumienski, Zbigniew (2014). "Microstates as Modern Protected States: Towards a New Definition of Micro-Statehood" (PDF). Occasional Paper. Centre for Small State Studies. Retrieved 2014-06-07.
3. ^ Mendelson, M. (1972). "Diminutive States in the United Nations". The International and Comparative Law Quarterly, 21(4), pp.609–630.
4. ^ Mehmet, O. & Tahiroglu, M., 2002. Growth and equity in microstates: Does size matter in development? International Journal of Social Economics, 29(1/2), pp.152–162.
5. ^ Boyce, P.J. & Herr, R.A., 2008. Microstate diplomacy in the south pacific. Australian Outlook, (April 2012), pp.37–41.
6. ^ Reid, G.L., 1975. Impact of Very Small Size on the International Behaviour of Microstates (International Studies), SAGE Publications Ltd.
7. ^ a b Neemia, U., 1995. Smallness, islandness and foreign policy behaviour: aspects of island microstates foreign policy behaviour with special reference to Cook Islands and Kiribati. University of Wollongong.
8. ^ Dommen, E., 1985. States, Microstates and Islands, Routledge Kegan & Paul.
9. ^ a b "CIA – The World Factbook – Rank Order – Population". CIA. Retrieved 2012-06-05.
10. ^ a b c Amstrup, N., 1976. The Perennial Problem of Small States: A Survey of Research Efforts. Cooperation and Conflict, 11(2), pp. 163–182.
11. ^ "CIA – The World Factbook – Rank Order – Area". CIA. Retrieved 2008-06-20.
12. ^ "Demographic Yearbook—Table 3: Population by sex, rate of population increase, surface area and density" (pdf). United Nations Statistics Division. 2008. Retrieved 2011-06-12.
13. ^ a b Neumann, I.B. & Gstöhl, S., 2004. Lilliputians in Gulliver’s World ? Small States in International Relations.
14. ^ Oest, K.J.N. & Wivel, A., 2010. Security, profit or shadow of the past? Explaining the security strategies of microstates. Cambridge Review of International Affairs, 23(3), pp. 429–453.

• Sack, John; Silverstein, Shel (1959). Report from practically nowhere. Harper.
Albania at the Olympics

Albania first participated at the Summer Olympic Games in 1972. They missed the next four games, two of them due to the 1980 and 1984 boycotts, but returned for the 1992 games in Barcelona. They have appeared in all games since then. They made their Winter Olympic Games debut in 2006. Albania normally competes in events that include swimming, athletics, weightlifting, shooting and wrestling. The country has not yet won an Olympic medal, and along with Bosnia and Herzegovina, it is the only European non-microstate without an Olympic medal. They have been represented by the Albanian National Olympic Committee since 1972.

Anarchism in Monaco

This is a short history of anarchism in Monaco, primarily in the late 19th century and early 20th century. Monaco, a principality formerly under the absolute rule of the House of Grimaldi and a constitutional monarchy since 1911, is located on the French Riviera in Western Europe. The city-state and microstate is bordered exclusively by France and the Mediterranean Sea.

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 bath, so that the states of the system will differ in total energy.

The principal thermodynamic variable of the canonical ensemble, determining the probability distribution of states, is the absolute temperature (symbol: T). The ensemble typically also depends on mechanical variables such as the number of particles in the system (symbol: N) and the system's volume (symbol: V), each of which influence the nature of the system's internal states. An ensemble with these three parameters is sometimes called the NVT ensemble.

The canonical ensemble assigns a probability P to each distinct microstate given by the following exponential:

${\displaystyle P=e^{\frac {F-E}{kT}},}$

where E is the total energy of the microstate, and k is Boltzmann's constant.

The number F is the free energy (specifically, the Helmholtz free energy) and is a constant for the ensemble. However, the probabilities and F will vary if different N, V, T are selected. The free energy F serves two roles: first, it provides a normalization factor for the probability distribution (the probabilities, over the complete set of microstates, must add up to one); second, many important ensemble averages can be directly calculated from the function F(N, V, T).

An alternative but equivalent formulation for the same concept writes the probability as

${\displaystyle \textstyle P={\frac {1}{Z}}e^{-E/(kT)},}$

using the canonical partition function

${\displaystyle \textstyle Z=e^{-F/(kT)}}$

rather than the free energy. The equations below (in terms of free energy) may be restated in terms of the canonical partition function by simple mathematical manipulations.

Historically, the canonical ensemble was first described by Boltzmann (who called it a holode) in 1884 in a relatively unknown paper. It was later reformulated and extensively investigated by Gibbs in 1902.

EEG microstates

EEG microstates are transient, patterned, quasi-stable states or patterns of an electroencephalogram. These tend to last anywhere from milliseconds to seconds and are hypothesized to be the most basic initializations of human neurological tasks, and are thus nicknamed "the atoms of thought". Microstate estimation and analysis was originally done using alpha band activity, though broader bandwidth EEG bands are now typically used. The quasi-stability of microstates means that the "global [EEG] topography is fixed, but strength might vary and polarity invert."

Ensemble average (statistical mechanics)

In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the microstate of a system (the ensemble of possible states), according to the distribution of the system on its micro-states in this ensemble.

Since the ensemble average is dependent on the ensemble chosen, its mathematical expression varies from ensemble to ensemble. However, the mean obtained for a given physical quantity doesn't depend on the ensemble chosen at the thermodynamic limit.

The grand canonical ensemble is an example of an open system.

Entropy (statistical thermodynamics)

In classical statistical mechanics, the entropy function earlier introduced by Rudolf Clausius is interpreted as statistical entropy using probability theory. The statistical entropy perspective was introduced in 1870 with the work of physicist Ludwig Boltzmann.

European microstates

The European microstates or European ministates are a set of very small sovereign states in Europe. The term is typically used to refer to the six smallest states in Europe by area: Andorra, Liechtenstein, Malta, Monaco, San Marino, and Vatican City. Four of these states are monarchies (three principalities—Andorra, Liechtenstein, and Monaco—and one papacy, the Vatican City), with all these states tracing their status back to the first millennium or the early second millennium, except for Liechtenstein, created in the 17th century.

Microstates are small independent states recognized by larger states, unlike micronations, which are only self-declared and not recognized. According to the qualitative definition suggested by Dumienski (2014), microstates can also be viewed as "modern protected states, i.e. sovereign states that have been able to unilaterally depute certain attributes of sovereignty to larger powers in exchange for benign protection of their political and economic viability against their geographic or demographic constraints." In line with this definition, only Andorra, Liechtenstein, San Marino, and Monaco qualify as "microstates" as only these states are sovereignties functioning in close, but voluntary, association with their respective larger neighbours. Luxembourg, which is much larger than all the European microstates combined, nonetheless shares some of these characteristics.Some scholars dispute the status of Vatican City as a state, arguing that it does not meet the "traditional criteria of statehood" and that the "special status of the Vatican City is probably best regarded as a means of ensuring that the Pope can freely exercise his spiritual functions, and in this respect is loosely analogous to that of the headquarters of international organisations."

Gibbons–Hawking space

In mathematical physics, a Gibbons–Hawking space, named after Gary Gibbons and Stephen Hawking, is essentially a hyperkähler manifold with an extra U(1) symmetry. (In general, Gibbons–Hawking metrics are a subclass of hyperkähler metrics.) Gibbons–Hawking spaces, especially ambipolar ones, find an application in the study of black hole microstate geometries.

History of Andorra

Andorra, officially the Principality of Andorra (Catalan: Principat d'Andorra), also called the Principality of the Valleys of Andorra (Catalan: Principat de les Valls d'Andorra), is a sovereign landlocked microstate in Southwestern Europe, located in the eastern Pyrenees mountains and bordered by Spain and France.

Kelmis

Kelmis (French: La Calamine) is a municipality located in the Belgian province of Liège, named for the historical deposits of calamine (zinc ore) nearby. As of 2011, the population was 10,881; the area is 18.1 square kilometres (7.0 sq mi) and the population density is 601.2 inhabitants per square kilometre (1,557/sq mi).The municipality consists of the following sub-municipalities: Kelmis proper, Hergenrath, and Neu-Moresnet.

The territory around the Vieille Montagne zinc mine in Kelmis was a neutral condominium of the Netherlands and Prussia (later Belgium and Germany) from 1816 to 1919 as Neutral Moresnet, with the Mayor of Kelmis being nominated by two commissioners from the neighbouring countries. Although there were attempts by locals at making it evolve into a fully independent microstate, all of them were thwarted and it remained under double-sovereignty and neutrality until its eventual annexation by Belgium after World War I.

In the nineteenth century a Low Dietsch dialect was spoken in Kelmis. Today Kelmis is bilingual: German and French and one of the nine municipalities of the German‑speaking Community of Belgium.

List of companies of Andorra

Andorra is a sovereign landlocked microstate in Southwestern Europe, located in the eastern Pyrenees mountains and bordered by Spain and France. Tourism, the mainstay of Andorra's economy, accounts for roughly 80% of GDP. An estimated 10.2 million tourists visit annually, attracted by Andorra's duty-free status and by its summer and winter resorts.

List of companies of Liechtenstein

Liechtenstein is a principality in the Alps and a microstate. Despite its small landmass of only 160 km² and a population of 38,111 Liechtenstein has a very successful industrial sector and a strong banking industry, making the country one of the most prosperous nations in the world. The domestic unemployment rate is 1,7 % and about 54% of all employees employed in Liechtenstein are commuters from neighbouring countries.

Microstate (statistical mechanics)

In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density. Treatments on statistical mechanics, define a macrostate as follows: a particular set of values of energy, the number of particles, and the volume of an isolated thermodynamic system is said to specify a particular macrostate of it. In this description, microstates appear as different possible ways the system can achieve a particular macrostate.

A macrostate is characterized by a probability distribution of possible states across a certain statistical ensemble of all microstates. This distribution describes the probability of finding the system in a certain microstate. In the thermodynamic limit, the microstates visited by a macroscopic system during its fluctuations all have the same macroscopic properties.

Microstate continuum

A microstate continuum is the fluctuation spectrum of a thermodynamic system in the classical limit of high temperatures. Classical here is to be understood in opposition to quantum statistical mechanics.

Partition function (statistical mechanics)

In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless, it is a pure number.

Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the environment at fixed temperature, volume, and number of particles. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for generalizations. The partition function has many physical meanings, as discussed in Meaning and significance.

Postage stamps and postal history of Liechtenstein

This is a survey of the postage stamps and postal history of Liechtenstein.

The Principality of Liechtenstein is a doubly landlocked Alpine microstate in Western Europe, bordered by Switzerland to the west and south and by Austria to the east. Its area is just over 160 square kilometres (62 sq mi), and it has an estimated population of 37,000. Its capital is Vaduz and the biggest town is Schaan.

The postal history of the principality pre-dates introduction of the first postage stamps in 1850. The principality was obliged to use Austrian stamps until 1912 when the first Liechtenstein issues were produced, although these were still issued under Austrian direction. Following the collapse of Habsburg Austria in 1918, Liechtenstein secured postal independence and began issuing its own stamps from July 1920.

SMtv San Marino (TV channel)

SMtv San Marino is the television station of SMtv San Marino, the national public service broadcaster of San Marino, an enclaved microstate surrounded by Italy.

The channel mostly shows self-produced entertainment programming. It is also part of Eurovision Network (broadcasting the Eurovision Song Contest) and the Italian television syndication K2. It also offers a Teletext service entitled, San Marino Video.

SMtv San Marino also is responsible for the Sammarinese participation in the Eurovision Song Contest. They debuted in 2008 with Miodio and placed last in the first semifinal, getting five points. After RAI, SMRTV also announced its comeback in the Eurovision Song Contest 2011. It reached the Grand Final in 2014 with Valentina Monetta's song Maybe and in 2019 with Serhat's song Say Na Na Na.

Sammarinese cuisine

As San Marino is a microstate completely landlocked by Italy, Sammarinese cuisine is strongly similar to the Italian cuisine, especially that of the adjoining Emilia-Romagna and Marche regions. San Marino's primary agricultural products are cheese, wine and livestock, and cheesemaking is a primary economic activity in San Marino. San Marino participated in The Exposition Universelle of 1889, a world's fair held in Paris, France, with three exhibits of oils and cheese.

San Marino RTV

San Marino RTV (Italian: Radiotelevisione della Repubblica di San Marino (San Marino RTV)) is the public service broadcaster of the microstate of San Marino.

San Marino RTV currently operates four television channels: San Marino RTV, San Marino RTV 2, San Marino RTV Sport and San Marino RTV Sat. It currently operates two radio stations, Radio San Marino and Radio San Marino Classic.

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