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Studying the implications and characterizations of the excited state quantumphase transitions (ESQPTs) would enable us to understand various phenomenaobserved in quantum many body systems.In this work, we delve into the affectsand characterizations of the ESQPTs in the anharmonic Lipkin-Meshkov-Glick(LMG) model by means of the entropy of the quantum work distribution. Theentropy of the work distribution measures the complexity of the workdistribution and behaves as a valuable tool for analyzing nonequilibrium workstatistics.We show that the entropy of the work distribution captures salientsignatures of the underlying ESQPTs in the model.In particular, a detailedanalyses of the scaling behavior of the maximal entropy verifies thatit acts asa witness of the ESQPTs. We further demonstrate that the entropy of the workdistribution also reveals the features of the ESQPTs in the energy space andcan be used to determine their critical energies. Our results provide furtherevidence of the usefulness of the entropy of the work distribution forinvestigating various phase transitions in quantum many body systems and openup a promising way for experimentally exploring the signatures of ESQPTs.

Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model