Dissipation in Hydrodynamics from Micro- to Macroscale: Wisdom from Boltzmann and Stochastic Thermodynamics

Abstract

We show that macroscopic irreversible thermodynamics for viscous fluids can be derived from exact information-theoretic thermodynamic identities valid at the microscale. Entropy production, in particular, is a measure of the loss of many-particle correlations in the same way in which it measures the loss of system-reservoirs correlations in stochastic thermodynamics (ST). More specifically, we first show that boundary conditions at the macroscopic level define a natural decomposition of the entropy production rate (EPR) in terms of thermodynamic forces multiplying their conjugate currents, as well as a change in suitable nonequilibrium potential that acts as a Lyapunov function in the absence of forces. Moving to the microscale, we identify the exact identities at the origin of these dissipative contributions for isolated Hamiltonian systems. We then show that the molecular chaos hypothesis, which gives rise to the Boltzmann equation at the mesoscale, leads to a positive rate of loss of many-particle correlations, which we identify with the Boltzmann EPR. By generalizing the Boltzmann equation to account for boundaries with nonuniform temperature and nonzero velocity, and resorting to the Chapman-Enskog expansion, we recover the macroscopic theory we started from. Finally, using a linearized Boltzmann equation we derive ST for dilute particles in a weakly out-of-equilibrium fluid and its corresponding macroscopic thermodynamics. Our work unambiguously demonstrates the information-theoretical origin of thermodynamic notions of entropy and dissipation in macroscale irreversible thermodynamics.

36 pages, 1 figure

References in corpus (39)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Dissipation: The phase-space perspective
• Entropy production as correlation between system and reservoir
• Three detailed fluctuation theorems
• Stochastic thermodynamics under coarse-graining
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• The Three Faces of the Second Law: I. Master Equation Formulation
• Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• Microscopic analysis of Clausius-Duhem processes
• Local detailed balance
• Information Thermodynamics of Turing Patterns
• Periodically modulated thermal convection
• Entropy Production in Open Systems: The Predominant Role of Intra-Environment Correlations
• Conservation Laws shape Dissipation
• Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
• Conservation Laws and Work Fluctuation Relations in Chemical Reaction Networks
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Derivation of Hydrodynamics from the Hamiltonian description of particle systems
• Thermodynamics of Chemical Waves
• Thermodynamic consistency of quantum master equations
• Nonequilibrium Thermodynamics of Non-Ideal Chemical Reaction Networks
• Revisiting the Glansdorff-Prigogine criterion for stability within irreversible thermodynamics
• Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles
• Local detailed balance across scales: from diffusions to jump processes and beyond
• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
• Is the Boltzmann equation reversible? A large deviation perspective on the irreversibility paradox
• Emergent second law for non-equilibrium steady states
• Thermodynamics of Concentration vs Flux Control in Chemical Reaction Networks
• Thermal Waves and Heat Transfer Efficiency Enhancement in Harmonically Modulated Turbulent Thermal Convection
• Entropy growth during free expansion of an ideal gas
• Microscopic approach to the macrodynamics of matter with broken symmetries
• Stochastic thermodynamics for kinetic equations

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