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We investigate the open dynamics of a chain of interacting spins using thequantized version of the GENERIC equation from classical out-of-equilibriumthermodynamics. We focus on both equilibrium and nonequilibrium scenarios forchains of different sizes. While in the equilibrium case we demonstrate thermalequilibration to the correct many-body Gibbs density matrix, in thenonequilibrium dynamics we show a ballistic-to-diffusive transition in thesteady-state energy current and a scaling that is consistent with Fourier's lawof heat transfer.

Dissipation in spin chains using quantized nonequilibrium thermodynamics