On the effect of entropy production rate on the implementation of flow regime


Аuthors

Khatuntseva O. N.1, 2

1. Korolev Rocket and Space Corporation «Energia», Korolev, Moscow region, Russia
2. Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow region, Russia

e-mail: olga.khatuntseva@rsce.ru

Abstract

Dissipative systems can be divided into two types: those in which the rate of entropy production tends to its minimum possible value (Prigogine's Minimum Entropy Production Principle), and those in which the rate of entropy production tends to its maximum possible value (Ziegler's Maximum Entropy Production Principle).
For a correct description of dissipative systems, a fundamental issue is the possibility of using equations to describe not only the amount of entropy produced in the system, but also the different nature of its production. Specifically, it is crucial that the equations describing the processes occurring in dissipative systems can characterize both the production of entropy near the equilibrium state and the production of entropy far from it.
The study of the two flow regimes allows us to say that the laminar regime corresponds to a process that is close to equilibrium (and is characterized by Prigogine's Minimum Entropy Production Principle), while the turbulent regime is far from equilibrium (and is characterized by Ziegler's Maximum Entropy Production Principle). At the kinetic level of description, this means that the turbulent regime is characterized by a strong influence of rare events, which can lead to multiple realizations of a random variable (such as velocity) at each point in time.
The account of the different nature of entropy production, starting already with the recording of the Liouville equation, allows to consistently pass to the “modified” Boltzmann equation and the “modified” system of the Navier-Stokes equations, which makes it possible to describe both laminar and turbulent flow regimes on the basis of the same equations. As a result, it is possible to analytically determine “laminar” and generalized “turbulent” solutions for classical problems of hydrodynamics.
This paper addresses a number of issues related to the sixth problem of Hilbert, which concerns the correctness of the transition from the description of the interaction of individual molecules based on Newton's equations to the description of fluid and gas mechanics based on the Navier-Stokes equations, which are mediated through the Liouville and Boltzmann equations.

Keywords:

principles of minimum and maximum entropy production, laminar and turbulent flow, Liouville, Boltzmann, and Navier-Stokes equations

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