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The Hamiltonian nature of the precessional dynamics of the classicalHeisenberg model leads to reciprocal interactions amongst the spins. Heisenbergspins are reciprocal in nature. In this work, we study the dynamics of anonequilibrium classical spin chain in which the neighbours interact through apurely non-reciprocal exchange coupling [EPL 60, 418 (2002)] which preservesrotational symmetry. The resultant dynamics conserves neither magnetization norenergy. We uncover other local conservation laws in their place in the extremecase of a strictly antisymmetric coupling. We show numerically that the modelundergoes an analogue of thermalization. We present results on the presence ofconserved quantities, their diffusive spreading and a hydrodynamic picture, andthe nature of the decorrelation front upon adding an initial perturbation tothe system.

Emergent hydrodynamics in a non-reciprocal classical isotropic magnet