  Is it possible to readily distinguish a system made by an Avogadro's number
of identical elements and one with a single additional one? Usually, the answer
to this question is negative but, in this work, we show that in
antiferromagnetic quantum spin rings a simple out-of-equilibrium experiment can
do so, yielding two qualitatively and quantitatively different outcomes
depending on whether the system includes an even or an odd number of elements.
We consider a local quantum-quench setup and calculate a generating function of
the work done, namely, the Loschmidt echo, showing that it displays different
features depending on the presence or absence of topological frustration, which
is triggered by the even/oddness in the number of the chain sites. We employ
the prototypical quantum Ising chain to illustrate this phenomenology, which we
argue being generic for antiferromagnetic spin chains, as it stems primarily
from the different low energy spectra of frustrated and non frustrated chains.
Our results thus prove that these well-known spectral differences lead indeed
to distinct observable characteristics and open the way to harvest them in
quantum thermodynamics protocols.
