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We focus on the biorthogonal work statistics of the interacting many-bodyHatano-Nelson model after switching on the imaginary vector potential. Weintroduce a generalized Loschmidt echo $G(t)$ utilizing the biorthogonal metricoperator. It is well suited for numerical analysis and its Fourier transformyields the probability distribution of work done. The statistics of workdisplays several universal features, including an exponential decay with thesquare of both the system size and imaginary vector potential for theprobability to stay in the ground state. Additionally, its high energy tailfollows a universal power law with exponent $-3$. This originates from thepeculiar temporal power law decay of $G(t)$ with a time dependent exponent. Themean and the variance of work scale linearly and logarithmically with systemsize while all higher cumulants are non-extensive. Our results are relevant fornon-unitary field theories as well.

Work statistics and generalized Loschmidt echo for the Hatano-Nelson model