12 research outputs found
Thermodynamics and Fluctuation Theorems for a Strongly Coupled Open Quantum System: An Exactly Solvable Case
We illustrate recent results concerning the validity of the work fluctuation
theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi,
Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable
model of an open quantum system. The central role played by the thermodynamic
partition function of the open quantum system, -- a two level fluctuator with a
strong quantum nondemolition coupling to a harmonic oscillator --, is
elucidated. The corresponding quantum Hamiltonian of mean force is evaluated
explicitly. We study the thermodynamic entropy and the corresponding specific
heat of this open system as a function of temperature and coupling strength and
show that both may assume negative values at nonzero low temperatures.Comment: 8 pages, 6 figure
Transient fluctuation theorem in closed quantum systems
Our point of departure are the unitary dynamics of closed quantum systems as
generated from the Schr\"odinger equation. We focus on a class of quantum
models that typically exhibit roughly exponential relaxation of some observable
within this framework. Furthermore, we focus on pure state evolutions. An
entropy in accord with Jaynes principle is defined on the basis of the quantum
expectation value of the above observable. It is demonstrated that the
resulting deterministic entropy dynamics are in a sense in accord with a
transient fluctuation theorem. Moreover, we demonstrate that the dynamics of
the expectation value are describable in terms of an Ornstein-Uhlenbeck
process. These findings are demonstrated numerically and supported by
analytical considerations based on quantum typicality.Comment: 5 pages, 6 figure
Quantum Fluctuation Relations for the Lindblad Master Equation
An open quantum system interacting with its environment can be modeled under
suitable assumptions as a Markov process, described by a Lindblad master
equation. In this work, we derive a general set of fluctuation relations for
systems governed by a Lindblad equation. These identities provide quantum
versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response
regime, these fluctuation relations yield a fluctuation-dissipation theorem
(FDT) valid for a stationary state arbitrarily far from equilibrium. For a
closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula
DFT-inspired methods for quantum thermodynamics
In the framework of quantum thermodynamics, we propose a method to
quantitatively describe thermodynamic quantities for out-of-equilibrium
interacting many-body systems. The method is articulated in various
approximation protocols which allow to achieve increasing levels of accuracy,
it is relatively simple to implement even for medium and large number of
interactive particles, and uses tools and concepts from density functional
theory. We test the method on the driven Hubbard dimer at half filling, and
compare exact and approximate results. We show that the proposed method
reproduces the average quantum work to high accuracy: for a very large region
of parameter space (which cuts across all dynamical regimes) estimates are
within 10% of the exact results