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

Understand

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.