AI summary · arXiv: 2306.00911v1 · cond-mat.stat-mech
Dissipation in Hydrodynamics from Micro- to Macroscale: Wisdom from Boltzmann and Stochastic Thermodynamics
The essentials
- The paper explores the relationship between microscopic, mesoscopic, and macroscopic formulations of nonequilibrium thermodynamics.
- Exact information-theoretic thermodynamic identities at the microscale are used to derive macroscopic irreversible thermodynamics for viscous fluids.
- Entropy production is identified as a measure of the loss of many-particle correlations, similar to its role in measuring system-reservoir correlations in stochastic thermodynamics (ST).
- Entropy production rate (EPR) at the macroscopic level is decomposed in terms of thermodynamic forces multiplied by their conjugated currents.
- A change in a nonequilibrium potential serves as a Lyapunov function in the absence of forces.
- Dissipative contributions at the microscale stem from exact identities for isolated Hamiltonian systems.
- The Boltzmann equation at the mesoscale leads to a positive rate of loss of many-particle correlations known as Boltzmann entropy production rate.
- Generalizing the Boltzmann equation accommodates boundaries with nonuniform temperature and nonzero velocity using Chapman--Enskog expansion, reproducing macroscopic theory successfully.
- A linearized Boltzmann equation adheres to local detailed balance (LDB), replicating ST theory at an equivalent mesoscale description.
- The study highlights the information-theoretical foundation underlying concepts like entropy and dissipation in macroscale irreversible thermodynamics, bridging different scales of thermodynamic descriptions.
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