The thermodynamic entropy of the Euler flow remains constant, following the rules of thermodynamics. Prof. Mahendra Verma and research scholar Soumyadeep Chatterjee from the Department of Physics, IIT Kanpur, introduced “hydrodynamic entropy” as a measure of order in a multiscale, nonequilibrium system like hydrodynamic and astrophysical systems and applied it to turbulence.
They found that 2D Euler flow, or flow with no viscosity, progresses from disorder to order. Analytical arguments and precise numerical simulations were used in this study, which offers insightful information that can improve how scientists approach crucially important fundamental subjects like order to disorder evolution, the second law of thermodynamics, and thermalization, the process by which physical processes achieve thermal equilibrium.
The two-dimensional Euler flow changes from order to disorder, and the system is out of equilibrium due to an intriguing energy exchange between the flow structures that violates the precise energy balance. The non-equilibrium behavior of 2D Euler turbulence is caused by an inverse cascade of energy.
Using hydrodynamic entropy to Euler turbulence, scientists have shown that the hydrodynamic entropy of 2D Euler flow decreases with time during its approach to the asymptotic state. The duo has also found that the final state of the flow depends critically on the initial condition.
The findings illustrate that the isolated dynamical system may evolve from disorder to order at macroscopic scales and that there is a need to be cautious of general claims on the “evolution from order to disorder” in any system. Based on their findings, Prof. Verma and Mr. Chatterjee believe that a similar evolution may occur in self-gravitating systems.
According to scientists, hydrodynamic entropy may be useful for quantifying order in biological, hydrodynamic, astrophysical, ecological, and economic systems.