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We use a first-principle quantum-statistical method to derive the expressionof the entropy production rate in relativistic spin hydrodynamics. We show thatthe entropy current is not uniquely defined and can be changed by means ofentropy-gauge transformations, much the same way as the stress-energy tensorand the spin tensor can be changed with pseudo-gauge transformations. We showthat the local thermodynamic relations, which are admittedly educated guessesin relativistic spin hydrodynamics inspired by those at global thermodynamicequilibrium, do not hold in general and they are also non-invariant underentropy-gauge transformations. Notwithstanding, we show that the entropyproduction rate is independent of those transformations and we provide auniversally applicable expression, extending that known in literature, fromwhich one can infer the dissipative parts of the energy momentum and spintensors.

Entropy current and entropy production in relativistic spin hydrodynamics