Abstract
The Leggett-Garg inequalities serve to test whether or not quantum correlations in time can be explained within a classical macrorealistic framework. We apply this test to thermodynamics and derive a set of Leggett-Garg inequalities for the statistics of fluctuating work done on a quantum system unitarily driven in time. It is shown that these inequalities can be violated in a driven two-level system, thereby demonstrating that there exists no general macrorealistic description of quantum work. These violations are shown to emerge within the standard Two-Projective-Measurement scheme as well as for alternative definitions of fluctuating work that are based on weak measurement. Our results elucidate the influences of temporal correlations on work extraction in the quantum regime and highlight a key difference between quantum and classical thermodynamics.
Highlights
Much like the celebrated Bell inequalities, which shed light on the deeply non-classical properties of spatial correlations encountered in entangled systems, quantum mechanics posseses a rich temporal structure that distinguishes it from classical physics
Following that we introduce an alternative set of Leggett-Garg inequalities for the moment-generating function, and apply these inequalities to alternative definitions of quantum work that are based on weak measurement, namely the full-counting statistics (FCS) and MH definitions, subsequently showing that violations of macrorealism can occur
In the paper we have demonstrated a violation of macrorealism in the statistics of fluctuating work for a quantum system unitarily driven out of thermal equilibrium for three different characterisations of the work statistics
Summary
Much like the celebrated Bell inequalities, which shed light on the deeply non-classical properties of spatial correlations encountered in entangled systems, quantum mechanics posseses a rich temporal structure that distinguishes it from classical physics. For a closed quantum system, one way of defining the fluctuating work done on the system driven out of equilibrium is by the difference in energy eigenvalues observed at the start and end of its evolution This framework is commonly referred to as the two-projective-measurement scheme, and serves as a route to many of the known fluctuation theorems such as the Jarzynski equality [15,16] and Tasaki-Crooks relation [18]. We show that quantum temporal correlations between energy measurements performed at different times influence the statistical moments of the fluctuating work done on the system during a non-equilibrium process This result is shown to hold for three different definitions of quantum work: the two-projective measurement (TPM) scheme [15], the full-counting statistics (FCS) [24] and the Margenau-Hill (MH) work distribution [23].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
