Contributions to single-shot energy exchanges in open quantum systems

Abstract

The exchange of energy between a classical open system and its environment can be analysed for a single run of an experiment using the phase space trajectory of the system. By contrast, in the quantum regime such energy exchange processes must be defined for an ensemble of runs of the same experiment based on the reduced system density matrix. Single-shot approaches have been proposed for quantum systems that are weakly coupled to a heat bath. However, a single-shot analysis for a quantum system that is entangled or strongly interacting with external degrees of freedom has not been attempted because no system wave function exists for such a system within the standard formulation of quantum theory. Using the notion of the conditional wave function of a quantum system, we derive here an exact formula for the rate of total energy change in an open quantum system, valid for arbitrary coupling between the system and the environment. In particular, this allows us to identify three distinct contributions to the total energy flow: an external contribution coming from the explicit time dependence of the Hamiltonian, an interaction contribution associated with the interaction part of the Hamiltonian, and an entanglement contribution, directly related to the presence of entanglement between the system and its environment. Given the close connection between weak values and the conditional wave function, the approach presented here provides a new avenue for experimental studies of energy fluctuations in open quantum systems.

Work exchange, geometric magnetization, and fluctuation-dissipation relations in a quantum dot under adiabatic magnetoelectric driving

“…By introducing a time-dependent component in this magnetic field, along with the variation of the gate voltage would lead to a scenario like the one studied in the present work. At finite T , the effects we have studied could be relevant in the implementation of driving protocols for thermal machines, [50][51][52][53][54][55][56] as well as in the discussion of shortcuts to adiabaticity. [57][58][59]…”

Correlation-enabled energy exchange in quantum systems without external driving

“…Within the framework of thermodynamics, it is possible to study different correlations such as system-environment correlation, correlation between different constituents of the system itself, or even correlations within the environment. It is known that system-environment correlation is an important element in the system's dynamical equation and accordingly in the thermodynamic properties of the system, e.g., in energy transfer [1][2][3][4]. In particular, in the strong coupling regime correlation comes into play indirectly through interactions [5,6].…”

Unreliability of mutual information as a measure for variations in total correlations

“…With recent developments in the rapidly growing field of quantum information science, numerous novel concepts have been introduced and used for a plethora of systems and applications in physics, communications, and computation [1,2], where correlations (quantum in particular) play a key role. For example, in quantum thermodynamics [3], it is known that correlations can be a resource in energy transfer [4,5], heat and work conversion [6][7][8][9][10], entropy exchange [11][12][13], and in the performance of quantum heat engines [14]. Correlations can also have implications on the size of the gap in the energy spectrum of correlated systems [15].…”