New effects in ideal gases solve mathematical mystery

A Mathematician from our Department of Mathematics, Professor Alexander Gorban, along with a physicist from ETH Zürich, Ilya Karlin, have challenged traditional concepts of micro and macro worlds and demonstrated how ideal gas unexpectedly exhibits capillarity properties.

In a paper published in the journal Contemporary Physics, they have paved the way to the solution of Hilbert’s 6th problem, a century-old mathematical mystery.

In 1900, David Hilbert published a list of problems which influenced the development of mathematics for a century. Generations of mathematicians have tried to solve Hilbert’s problems, but a few remained unsolved. The 6th problem remains a big challenge for the scientific community.

Hilbert hypothesised that the problem is in the creation of a rigorous link between atomistic dynamics and the famous Navier-Stokes equations of fluid dynamics. Many big names in mathematics have tried to find conditions under which this link exists. So far, this link has only been established for infinitely slow and almost uniform fluid flows.

Gorban and Karlin in a series of works demonstrated that this is not the general case, and for the non-equilibrium flows the well-known equations should be corrected.

Professor Gorban said: “In high school textbooks and the popular science literature, capillarity is attributed to a liquid. How does capillarity appear in ideal gas? The answer to this question is in the nature of the interfaces between `bricks of matter’ used in the foundations of classical continuum mechanics.”

The results of Gorban and Karlin’s research can be considered as the negative answer to Hilbert’s 6th problem and brings insights to microfluidic and nanofluidic engineering.

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