Nonequilibrium thermodynamics of turbulence and stochastic fluid systems

Abstract

Fluid systems are found in the Universe at various scales. Turbulence as a complex form of fluid motion far from thermodynamic equilibrium remains one of the most challenging problems in physics. In this work, we study the nonequilibrium thermodynamics of stochastic fluid systems in general and turbulence in particular. Our approach is based on a reinterpretation of the stochastic fluid system as an interacting many-body system in contact with multiple heat baths. A set of nonequilibrium thermodynamic equations for general stochastic fluid systems, applicable to turbulence in the far-from-equilibrium regime, is constructed using the potential landscape and flux field theory. In addition to the energy and entropy balance equations that represent the first and second laws of thermodynamics, a new thermodynamic equation is found to be crucial for relating the first law with the second law and connecting violation of detailed balance to entropy flow and entropy production at the steady state. It is demonstrated that steady-state entropy production and energy flow are manifestations of the nonequilibrium irreversible nature of fluid systems characterized by the nonequilibrium trinity construct that originates from temperature nonuniformity. We propose an intuitive thermodynamic picture of the turbulence energy cascade process as heat conduction in the scale domain, where energy flow across scales is conducted by nonlinear convection and driven by the temperature difference between the large and small scales. Nonequilibrium irreversibility of turbulence energy cascade is quantified by the steady-state entropy production rate. This work is rooted in both fluid dynamics and nonequilibrium statistical physics, fostering a deeper level of communication between these fields. Further extensions of this work have the potential to grow into a more complete nonequilibrium statistical theory, with a much wider range of applications encompassing general physical, chemical and biological nonequilibrium systems.