Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements

The authors are indebted to T. S. Batalhao, J. Goold, R. Serra, and Peter Talkner for invaluable discussions.
We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.
This work has been supported by a PERFEST grant (L. F.) from Universita degli Studi di Palermo, the Marie Curie Action, the UK EPSRC (EP/G004579/1 and EP/ L005026/1), the John Templeton Foundation (Grant ID 43467), the EU Collaborative Project TherMiQ (Grant Agreement No. 618074), and by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme through the project NeQuFlux Grant No. 623085 (M. C.). T. J. G. A. is supported by the European Commission, the European Social Fund, and the Region Calabria through the program POR Calabria FSE 2007-2013-Asse IV Capitale Umano-Obiettivo Operativo M2. A. X. acknowledges funding from the Royal Commission for the Exhibition of 1851. Part of this work was supported by the COST Action MP1209 “Thermodynamics in the Quantum Regime.”
peer-reviewed