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We show that macroscopic irreversible thermodynamics for viscous fluids canbe derived from exact information-theoretic thermodynamic identities valid atthe microscale. Entropy production, in particular, is a measure of the loss ofmany-particle correlations in the same way in which it measures the loss ofsystem-reservoirs correlations in stochastic thermodynamics (ST). Morespecifically, we first show that boundary conditions at the macroscopic leveldefine a natural decomposition of the entropy production rate (EPR) in terms ofthermodynamic forces multiplying their conjugated currents, as well as a changein suitable nonequilibrium potential that acts as a Lyapunov function in theabsence of forces. Moving to the microscale, we identify the exact identitiesat the origin of these dissipative contributions for isolated Hamiltoniansystems. We then show that the molecular chaos hypothesis, which gives rise tothe Boltzmann equation at the mesoscale, leads to a positive rate of loss ofmany-particle correlations, which we identify with the Boltzmann EPR. Bygeneralizing the Boltzmann equation to account for boundaries with nonuniformtemperature and nonzero velocity, and resorting to the Chapman--Enskogexpansion, we recover the macroscopic theory we started from. Finally, using alinearized Boltzmann equation we derive ST for dilute particles in a weaklyout-of-equilibrium fluid and its corresponding macroscopic thermodynamics. Ourwork unambiguously demonstrates the information-theoretical origin ofthermodynamic notions of entropy and dissipation in macroscale irreversiblethermodynamics.

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