| Summary: | We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied for two-level systems, while this is generally no longer true for <i>N</i>-level systems, with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>N</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula>. Focusing on three-level systems, we discuss the occurrence of a unique energy scale factor <inline-formula> <math display="inline"> <semantics> <msub> <mi>β</mi> <mi>eff</mi> </msub> </semantics> </math> </inline-formula> that formally plays the role of an effective inverse temperature in the Jarzynski equality. To this aim, we introduce a suitable parametrization of the initial state in terms of a thermal and a non-thermal component. We determine the value of <inline-formula> <math display="inline"> <semantics> <msub> <mi>β</mi> <mi>eff</mi> </msub> </semantics> </math> </inline-formula> for a large number of measurements and study its dependence on the initial state. Our predictions could be checked experimentally in quantum optics.
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