Heat-exchange statistics in driven open quantum systems

Abstract

As the dimensions of physical systems approach the nanoscale, the laws of thermodynamics must be reconsidered due to the increased importance of fluctuations and quantum effects. While the statistical mechanics of small classical systems is relatively well understood, the quantum case still poses challenges. Here we set up a formalism that allows to calculate the full probability distribution of energy exchanges between a periodically driven quantum system and a thermalized heat reservoir. The formalism combines Floquet theory with a generalized master equation approach. For a driven two-level system and in the long-time limit, we obtain a universal expression for the distribution, providing clear physical insight into the exchanged energy quanta. We illustrate our approach in two analytically solvable cases and discuss the differences in the corresponding distributions. Our predictions could be directly tested in a variety of systems, including optical cavities and solid-state devices.

22 pages, 2 figures

References in corpus (18)

• Fluctuation theorems: Work is not an observable
• Single ion heat engine with maximum efficiency at maximum power
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Experimental study of mutual information in a Maxwell Demon
• Thermodynamical Control by Frequent Quantum Measurements
• Counting Statistics of Non-Markovian Quantum Stochastic Processes
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Coherence times of dressed states of a superconducting qubit under extreme driving
• Employing trapped cold ions to verify the quantum Jarzynski equality
• Minimal universal quantum heat machine
• Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects
• Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
• Full counting statistics of nano-electromechanical systems
• Experimental free energy measurements of kinetic molecular states using fluctuation theorems
• Fluctuation theorems in driven open quantum systems
• Electron Waiting Times in Non-Markovian Quantum Transport
• Work and its fluctuations in a driven quantum system
• Environment-governed dynamics in driven quantum systems

Cited by in corpus (7)

• Fast electron thermometry towards ultra-sensitive calorimetric detection
• Coherence-enhanced efficiency of feedback-driven quantum engines
• Functional Integral approach to time-dependent heat exchange in open quantum systems: general method and applications
• Stochastic thermodynamics of rapidly driven systems
• Incomplete measurement of work in a dissipative two level system
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics