Deviation of a system of nonreciprocally coupled harmonic oscillators from a conservative system

Discrete systems of coupled linear mechanical oscillators with nonreciprocal interaction are a model for a variety of physical systems. In general, the presence of nonreciprocal interactions renders their dynamics nonconservative, but under certain conditions it remains conservative. In this paper we show which thermodynamic properties induced by nonreciprocity can be observed in conservative systems and which are specific to nonconservative systems. To this end, we formulate a criterion for identifying conservative systems and construct a measure to quantify the deviation from conservativity.