Nonreciprocal transmission through acoustic Tesla valve filled with viscous fluid

Attenuation of sound is a viscous fluid is a signature of irreducible process accompanied by increase of entropy. Presence of elastic scatterers adds non-dissipative contribution to attenuation. If the scatterers are symmetrically distributed between emitter and receiver (P symmetrical system), sound transmission emitter ↔ receiver remains reciprocal, although it is irreducible in each direction. From the pioneering work by Rayleigh, it is known that acoustic pressure is a reciprocal quantity even in a viscous fluid and non-symmetric distribution of scatterers. This property makes sound transmission an exclusion from the general mechanical principle requiring nonreciprocal dynamics if time-reversal symmetry (T symmetry) is broken. Here we demonstrate that acoustic intensity is a truly nonreciprocal quantity if PT symmetry is broken. As an example of an acoustic system with strongly broken P symmetry, we consider a Tesla valve filled with liquids of different viscosity, thus presenting mechanical systems with different levels of broken T symmetry. Experimental spectra for intensity confirm our theoretical conclusion about nonreciprocal wave dynamics in the systems with broken PT symmetry. Considering viscosity coefficient η as a nonreciprocal parameter, we show that replacement η→-η does not restore reciprocity, i.e., transmission through a viscous fluid does not possess Onsager symmetry. [Work supported by the NSF Grant No. 1741677 and by the AFOSR Grant FA9550-23-1-0630.]