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Topic · Statistical and Nonlinear Physics

Statistical Mechanics and Entropy

Statistical Mechanics and Entropy is a research topic within Statistical and Nonlinear Physics. Science Explorer counts 18k research works in it since 1950. 10.3% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the statistical mechanics of systems with long-range interactions and nonextensive behavior, characterized by Tsallis statistics, generalized entropies, superstatistics, non-Gaussian statistics, and anomalous diffusion. It explores the thermodynamic equilibrium, Fokker-Planck equations, and phase transitions in such systems.

  • Nonextensive Statistical Mechanics
  • Long-Range Interactions
  • Tsallis Statistics
  • Generalized Entropies
  • Superstatistics
  • Non-Gaussian Statistics
  • Anomalous Diffusion
  • Thermodynamic Equilibrium
  • Fokker-Planck Equations
  • Phase Transitions
Research works
18k
fractional, since 1950
In the world top 10%
1.8k
per year above
Top-10% rate
10.3%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-6%
the tick is no change
Largest producer
United States
24% of the 10 largest, 2022-now
Statistical Mechanics and Entropy

Which countries lead Statistical Mechanics and Entropy research?

By volume, the United States and China publish the most (405 and 265 works in 2022-now).

By volume, 2022-now

  1. 1 United States 405 works
  2. 2 China 265 works
  3. 3 India 177 works
  4. 4 Italy 131 works
  5. 5 France 129 works
  6. 6 United Kingdom 125 works
  7. 7 Germany 115 works
  8. 8 Japan 114 works
  9. 9 Brazil 102 works
  10. 10 Russia 101 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 24.3%China: 16.0%India: 10.6%Italy: 7.9%6 others listed: 41.2%24%largest
United States405 · 24.3%China265 · 16.0%India177 · 10.6%Italy131 · 7.9%6 others listed686 · 41.2%

Shares of the rows listed above, not of the whole node.

Which institutions lead Statistical Mechanics and Entropy research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Statistical Mechanics and Entropy research, followed by Russian Academy of Sciences and National University of Singapore.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 52 works
  2. 2 Russian Academy of SciencesRussia 40 works
  3. 3 National University of SingaporeSingapore 23 works
  4. 4 Chinese Academy of SciencesChina 17 works
  5. 5 Sapienza University of RomeItaly 16 works
  6. 6 The University of TokyoJapan 13 works
  7. 7 Max Planck SocietyGermany 11 works
  8. 8 Consejo Nacional de Investigaciones Científicas y TécnicasArgentina 11 works
  9. 9 Universidade de São PauloBrazil 10 works
  10. 10 National Academy of Sciences of UkraineUkraine 10 works

Who are the leading researchers in Statistical Mechanics and Entropy?

The most-cited researchers publishing on Statistical Mechanics and Entropy include Yoshua Bengio, Karl John Friston and Trevor Hastie.

  1. 1 Yoshua Bengio Canada 476k citations
  2. 2 Karl John Friston United Kingdom 310k citations
  3. 3 Trevor Hastie United States 301k citations
  4. 4 Xiaogang Wang China 260k citations
  5. 5 Vladimir N. Vapnik United States 227k citations
  6. 6 David H. Haussler United States 209k citations
  7. 7 Harry Eugene Stanley United States 198k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Statistical Mechanics and Entropy?

The most cited paper in Statistical Mechanics and Entropy is "Canonical dynamics: Equilibrium phase-space distributions" (William Graham Hoover, 1985), with 23,918 citations. Next come "Information Theory and an Extension of the Maximum Likelihood Principle" (18,124) and "Information Theory and Statistical Mechanics" (13,114).

Most cited papers
#PaperReleasedCitations
1 Canonical dynamics: Equilibrium phase-space distributions William Graham Hoover · Physical Review A Mar 1985 23,918
2 Information Theory and an Extension of the Maximum Likelihood Principle Hirotogu Akaike · Springer series in statistics Book chapter 1998 18,124
3 Information Theory and Statistical Mechanics E. T. Jaynes · Physical Review 15 May 1957 13,114
4 emcee : The MCMC Hammer Daniel Foreman-Mackey, David W. Hogg, Dustin Lang et al. · Publications of the Astronomical Society of the Pacific Open access Mar 2013 12,323
5 Possible generalization of Boltzmann-Gibbs statistics Constantino Tsallis · Journal of Statistical Physics Jul 1988 9,702
All 100 most cited papers, with filters and sorting

Where is Statistical Mechanics and Entropy research done?

The largest centres of Statistical Mechanics and Entropy research in 2022-now are Beijing (China), Paris (France), Moscow (Russia) and Tokyo (Japan).

Largest cities, 2022-now

  1. 1 BeijingChina 52 works
  2. 2 ParisFrance 52 works
  3. 3 MoscowRussia 50 works
  4. 4 TokyoJapan 42 works
  5. 5 LondonUnited Kingdom 35 works
  6. 6 RomeItaly 30 works
  7. 7 SingaporeSingapore 28 works
  8. 8 New YorkUnited States 28 works
  9. 9 Rio de JaneiroBrazil 22 works
  10. 10 MadridSpain 19 works
See Statistical Mechanics and Entropy on the map

Where is the best place to study Statistical Mechanics and Entropy?

Among universities, judged by research, Princeton University, National University of Singapore and University of Oxford score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 15.33%fractional works in this field (log) →share of work in the world top 10% →Princeton UniversityUniversity of OxfordSapienza University …National University …
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Princeton UniversityUnited States 65.743.6%9.6×9 +35.5%
2National University of SingaporeSingapore 59.21.7%8.9×23 +705.9%
3University of OxfordUnited Kingdom 42.324.6%3.0×9 +7.3%
4Sapienza University of RomeItaly 40.515.4%6.3×16 -17.6%
5Politecnico di TorinoItaly 38.114.3%8.7×9 +25.4%
6The University of TokyoJapan 33.214.3%4.9×13 -9.8%
7National Intelligence UniversityUnited States 25.38.6%489.4×8 -
8Massachusetts Institute of TechnologyUnited States 23.013.2%5.2×8 -33.4%
9Lomonosov Moscow State UniversityRussia 16.17.8%4.5×8 -32.9%
10Universidade de São PauloBrazil 16.09.8%2.3×10 -38.0%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Statistical Mechanics and Entropy, country by country

Is Statistical Mechanics and Entropy research growing?

Output in 2022-2025 was 6% lower than in 2018-2021, peaking in 2026.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Statistical Mechanics and Entropy as a percentage of every work published that year, 0.0074% in 2024.

still counting0.020%0.040%0.060%Statistical Mechanics and Entropy0.010% in 202519801990200020102020

Fractional works of Statistical Mechanics and Entropy over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Statistical Mechanics and Entropy11.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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