Quantum Crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir

Source: arXiv


We consider the quantum mechanical generalization of Crooks Fluctuation Theorem and Jarzynski Equality for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems beyond linear response theory regime.

Full-text preview

Available from: ArXiv
  • Source
    • "When the baths are thermal, the Carnot efficiency limit is equally applicable for a small quantum system [1] [2]. Even classical fluctuation theorems hold without any alteration [3] [4] [5]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: Quantum heat engines (QHE) are thermal machines where the working substance is a quantum object. In the extreme case, the working medium can be a single particle or a few-level quantum system. The study of QHE has shown a remarkable similarity with macroscopic thermodynamical results, thus raising the issue of what is quantum in quantum thermodynamics. Our main result is the thermodynamical equivalence of all engine types in the quantum regime of small action with respect to Planck's constant. They have the same power, the same heat, and the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown that QHE have quantum-thermodynamic signature; i.e., thermodynamic measurements can confirm the presence of quantum effects in the device. We identify generic coherent and stochastic work extraction mechanisms and show that coherence enables power outputs that greatly exceed the power of stochastic (dephased) engines.
    Physical Review X 09/2015; 5(3). DOI:10.1103/PhysRevX.5.031044 · 9.04 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.
    Physical Review E 05/2009; 79(4 Pt 1):041129. DOI:10.1103/PhysRevE.79.041129 · 2.29 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.
    Pramana 02/2012; 80(2). DOI:10.1007/s12043-012-0471-6 · 0.65 Impact Factor
Show more