--- title: "Heat, chance and collective behaviour" description: "How do atoms make a liquid, why does climate remember heat, and how can a network recall a picture? Follow the experiments and ideas through fourteen bilingual articles and four interactive models." canonical_url: "https://sandboxphysics.com/stories/thermal-complexity/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/thermal-complexity/" last_modified: "2026-10-24" --- 14 readings · Four interactive models · English and Chinese # Heat, chance and collective behaviour How do atoms make a liquid, why does climate remember heat, and how can a network recall a picture? Follow the experiments and ideas through fourteen bilingual articles and four interactive models. Try a change and see what follows ## Four ways to make the physics move 1. [Watch magnetic domains compete Change temperature and size, then sample the fluctuations.](https://sandboxphysics.com/labs/ising-critical-fluctuations/) 2. [Recover a damaged memory Erase part of a picture and let the network update.](https://sandboxphysics.com/labs/hopfield-associative-memory/) 3. [Follow heat into the ocean Change the forcing and compare surface and deep-ocean warming.](https://sandboxphysics.com/labs/climate-energy-balance/) 4. [Pluck a magnetic field Send a wave through a conducting fluid and change its speed.](https://sandboxphysics.com/labs/alfven-wave/) Reading path · D-R1 ## What a gas can tell us about atoms A small discrepancy in a balance, a disappearing liquid surface, and grains suspended in water each opened a different route to matter too small to see. 1. ### [The extra weight that revealed argon](https://sandboxphysics.com/stories/thermal-complexity/rayleigh-argon-density/) How did weighing nitrogen reveal another gas in the air? 2. ### [How a gas becomes a liquid and loses the boundary](https://sandboxphysics.com/stories/thermal-complexity/van-der-waals-critical-point/) What must an ideal-gas picture gain before it can explain condensation? 3. ### [Perrin counted the grains that refused to settle](https://sandboxphysics.com/stories/thermal-complexity/perrin-sedimentation/) How could visible particles reveal the molecular scale of water? 4. ### [Bridgman opened the way into matter under pressure](https://sandboxphysics.com/stories/thermal-complexity/bridgman-high-pressure/) What did a better seal let physicists learn about compressed matter? Reading path · D-R2 ## How order survives, changes and gets frustrated Near a critical point, small patches join larger ones. Long molecules coil, liquid crystals align, and competing magnetic bonds make agreement impossible. 1. ### [Why very different materials behave alike near a critical point](https://sandboxphysics.com/stories/thermal-complexity/wilson-critical-scales/) How did Wilson make sense of fluctuations at many different sizes? 2. ### [A liquid can flow and still keep a direction](https://sandboxphysics.com/stories/thermal-complexity/de-gennes-liquid-crystals/) What kind of order survives when a liquid crystal flows? 3. ### [A long molecule behaves like a wandering chain](https://sandboxphysics.com/stories/thermal-complexity/polymer-scaling/) Why does the size of a polymer coil depend on more than its total length? 4. ### [The magnets that cannot satisfy all their neighbours](https://sandboxphysics.com/stories/thermal-complexity/parisi-spin-glass/) What did Parisi discover in the apparently disordered states of a spin glass? Reading path · D-R3a ## Why climate responds slowly to a changing atmosphere Follow heat through a vertical column of air, then into an ocean that remembers yesterday’s weather. The two stories answer different parts of the climate problem. 1. ### [Manabe and Wetherald followed heat through the atmosphere](https://sandboxphysics.com/stories/thermal-complexity/manabe-radiative-convective/) How could a single column of air reveal the warming caused by more carbon dioxide? 2. ### [How the ocean remembers changing weather](https://sandboxphysics.com/stories/thermal-complexity/hasselmann-weather-climate/) How can rapidly changing weather produce slowly changing climate? Reading path · D-R3b ## When a network can remember and learn A damaged picture can settle back into a stored pattern. Adding random changes lets related networks learn which patterns are common. 1. ### [How a Hopfield network finds a damaged memory](https://sandboxphysics.com/stories/thermal-complexity/hopfield-energy-memory/) How can simple on-or-off units recover a whole pattern from an incomplete cue? 2. ### [How a Boltzmann machine learns which patterns belong together](https://sandboxphysics.com/stories/thermal-complexity/hinton-boltzmann-learning/) Why would a learning network benefit from making random changes? Reading path · D-R4 ## A valve in sunlight, a wave along a magnetic field A lighthouse valve compares how rods warm in daylight. A magnetic field pulls a conducting fluid back when it bends. In each case, the mechanism tells you what to measure. 1. ### [The rods that switched a lighthouse off at dawn](https://sandboxphysics.com/stories/thermal-complexity/dalen-sun-valve/) How did Dalén’s sun valve respond to daylight without electricity? 2. ### [A bent magnetic field can carry a wave](https://sandboxphysics.com/stories/thermal-complexity/alfven-magnetic-tension/) How can a magnetic field restore the motion of a conducting fluid? ## The work came before the prize Each date below marks a paper or experiment discussed in the reading. Prize dates appear separately; the articles introduce collaborators and the earlier work they built on. Open the discovery timeline 1. 1873 [How a gas becomes a liquid and loses the boundary](https://sandboxphysics.com/stories/thermal-complexity/van-der-waals-critical-point/) Nobel Prize: 1910 2. 1894 [The extra weight that revealed argon](https://sandboxphysics.com/stories/thermal-complexity/rayleigh-argon-density/) Nobel Prize: 1904 3. 1907 [The rods that switched a lighthouse off at dawn](https://sandboxphysics.com/stories/thermal-complexity/dalen-sun-valve/) Nobel Prize: 1912 4. 1908 [Perrin counted the grains that refused to settle](https://sandboxphysics.com/stories/thermal-complexity/perrin-sedimentation/) Nobel Prize: 1926 5. 1912 [Bridgman opened the way into matter under pressure](https://sandboxphysics.com/stories/thermal-complexity/bridgman-high-pressure/) Nobel Prize: 1946 6. 1942 [A bent magnetic field can carry a wave](https://sandboxphysics.com/stories/thermal-complexity/alfven-magnetic-tension/) Nobel Prize: 1970 7. 1967 [Manabe and Wetherald followed heat through the atmosphere](https://sandboxphysics.com/stories/thermal-complexity/manabe-radiative-convective/) Nobel Prize: 2021 8. 1971 [Why very different materials behave alike near a critical point](https://sandboxphysics.com/stories/thermal-complexity/wilson-critical-scales/) Nobel Prize: 1982 9. 1972 [A liquid can flow and still keep a direction](https://sandboxphysics.com/stories/thermal-complexity/de-gennes-liquid-crystals/) Nobel Prize: 1991 10. 1972 [A long molecule behaves like a wandering chain](https://sandboxphysics.com/stories/thermal-complexity/polymer-scaling/) Nobel Prize: 1991 11. 1976 [How the ocean remembers changing weather](https://sandboxphysics.com/stories/thermal-complexity/hasselmann-weather-climate/) Nobel Prize: 2021 12. 1979 [The magnets that cannot satisfy all their neighbours](https://sandboxphysics.com/stories/thermal-complexity/parisi-spin-glass/) Nobel Prize: 2021 13. 1982 [How a Hopfield network finds a damaged memory](https://sandboxphysics.com/stories/thermal-complexity/hopfield-energy-memory/) Nobel Prize: 2024 14. 1985 [How a Boltzmann machine learns which patterns belong together](https://sandboxphysics.com/stories/thermal-complexity/hinton-boltzmann-learning/) Nobel Prize: 2024 Find the eleven Nobel contributions ### [1904-1](https://www.nobelprize.org/prizes/physics/1904/summary/) Lord Rayleigh - [The extra weight that revealed argon](https://sandboxphysics.com/stories/thermal-complexity/rayleigh-argon-density/) ### [1910-1](https://www.nobelprize.org/prizes/physics/1910/summary/) Johannes Diderik van der Waals - [How a gas becomes a liquid and loses the boundary](https://sandboxphysics.com/stories/thermal-complexity/van-der-waals-critical-point/) ### [1912-1](https://www.nobelprize.org/prizes/physics/1912/summary/) Gustaf Dalén - [The rods that switched a lighthouse off at dawn](https://sandboxphysics.com/stories/thermal-complexity/dalen-sun-valve/) ### [1926-1](https://www.nobelprize.org/prizes/physics/1926/summary/) Jean Baptiste Perrin - [Perrin counted the grains that refused to settle](https://sandboxphysics.com/stories/thermal-complexity/perrin-sedimentation/) ### [1946-1](https://www.nobelprize.org/prizes/physics/1946/summary/) Percy W. Bridgman - [Bridgman opened the way into matter under pressure](https://sandboxphysics.com/stories/thermal-complexity/bridgman-high-pressure/) ### [1970-1](https://www.nobelprize.org/prizes/physics/1970/summary/) Hannes Alfvén - [A bent magnetic field can carry a wave](https://sandboxphysics.com/stories/thermal-complexity/alfven-magnetic-tension/) ### [1982-1](https://www.nobelprize.org/prizes/physics/1982/summary/) Kenneth G. Wilson - [Why very different materials behave alike near a critical point](https://sandboxphysics.com/stories/thermal-complexity/wilson-critical-scales/) ### [1991-1](https://www.nobelprize.org/prizes/physics/1991/summary/) Pierre-Gilles de Gennes - [A liquid can flow and still keep a direction](https://sandboxphysics.com/stories/thermal-complexity/de-gennes-liquid-crystals/) - [A long molecule behaves like a wandering chain](https://sandboxphysics.com/stories/thermal-complexity/polymer-scaling/) ### [2021-1](https://www.nobelprize.org/prizes/physics/2021/summary/) Syukuro Manabe · Klaus Hasselmann - [Manabe and Wetherald followed heat through the atmosphere](https://sandboxphysics.com/stories/thermal-complexity/manabe-radiative-convective/) - [How the ocean remembers changing weather](https://sandboxphysics.com/stories/thermal-complexity/hasselmann-weather-climate/) ### [2021-2](https://www.nobelprize.org/prizes/physics/2021/summary/) Giorgio Parisi - [The magnets that cannot satisfy all their neighbours](https://sandboxphysics.com/stories/thermal-complexity/parisi-spin-glass/) ### [2024-1](https://www.nobelprize.org/prizes/physics/2024/summary/) John Hopfield · Geoffrey Hinton - [How a Hopfield network finds a damaged memory](https://sandboxphysics.com/stories/thermal-complexity/hopfield-energy-memory/) - [How a Boltzmann machine learns which patterns belong together](https://sandboxphysics.com/stories/thermal-complexity/hinton-boltzmann-learning/) ## A few words you will meet Open the glossary - **Critical point**: The end of the liquid–gas coexistence curve. Above it, liquid and gas can change into one another continuously. - **Fluctuation**: A quantity’s spontaneous changes around its average, such as the changing magnetization of a warm lattice. - **Correlation length**: The distance over which a local change tends to be accompanied by changes elsewhere. - **Universality**: Systems with different microscopic details can share the same critical scaling when dimension, symmetry and interaction range agree. - **Nematic order**: Elongated molecules tend to point along one common axis even though their centres do not form a crystal lattice. - **Frustration**: Competing preferences cannot all be satisfied at once. Three spins with pairwise opposite preferences provide a simple example. - **Radiative forcing**: A change in Earth’s incoming-minus-outgoing energy flow, evaluated with a specified adjustment convention. - **Climate feedback**: Warming changes radiation, water vapour, clouds or ice, which in turn changes how quickly heat escapes. - **Associative memory**: A stored pattern can be recovered from an incomplete or corrupted cue. - **Energy landscape**: A way to picture each network configuration as a height. Updates can descend into different local valleys. - **Magnetic tension**: A bent magnetic field exerts a restoring force along its curvature in a conducting fluid. - **Ideal magnetohydrodynamics**: A continuum description of a conducting fluid in the limit where electrical resistivity is negligible on the scales considered. ## Continue into neighbouring questions [Magnetism, superconductors and material devices](https://sandboxphysics.com/stories/condensed-matter/) [Quantum physics and the experiments behind it](https://sandboxphysics.com/stories/quantum-evidence/) [How light and particles measure matter](https://sandboxphysics.com/stories/probe-evidence/)