[en] Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.
Disciplines :
Physics
Author, co-author :
Alipour, S.; QTF Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
Rezakhani, A. T.; Department of Physics, Sharif University of Technology, Tehran 14588, Iran
Chenu, Aurélia ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Del Campo Echevarria, Adolfo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Ala-Nissila, T.; QTF Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland ; Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
External co-authors :
yes
Language :
English
Title :
Entropy-based formulation of thermodynamics in arbitrary quantum evolution
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Heat is associated with entropy change. Note that (Equation presented), where (Equation presented) is a resolution of the identity, (Equation presented) and (Equation presented) constitutes probabilities, and (Equation presented)is the Shannon entropy [V. Vedral, Classical Correlations and Entanglement in Quantum Measurements, Phys. Rev. Lett. 90, 050401 (2003) 10.1103/PhysRevLett.90.050401].
The optimal measurement minimizing the Shannon entropy is given by the eigenvectors of (Equation presented); (Equation presented).
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