614 research outputs found
Open system trajectories specify fluctuating work but not heat
Based on the explicit knowledge of a Hamiltonian of mean force, the classical
statistical mechanics and equilibrium thermodynamics of open systems in contact
with a thermal environment at arbitrary interaction strength can be formulated.
Even though the Hamiltonian of mean force uniquely determines the equilibrium
phase space probability density of a strongly coupled open system the knowledge
of this probability density alone is insufficient to determine the Hamiltonian
of mean force, needed in constructing the underlying statistical mechanics and
thermodynamics. We demonstrate that under the assumption that the Hamiltonian
of mean force is known, an extension of thermodynamic structures from the level
of averaged quantities to fluctuating objects (i.e. a stochastic
thermodynamics) is possible. However, such a construction undesirably involves
also a vast ambiguity. This situation is rooted in the eminent lack of a
physical guiding principle allowing to distinguish a physically meaningful
theory out of a multitude of other equally conceivable ones.Comment: 12 pages, further typos correcte
The Tasaki-Crooks quantum fluctuation theorem
Starting out from the recently established quantum correlation function
expression of the characteristic function for the work performed by a force
protocol on the system [cond-mat/0703213] the quantum version of the Crooks
fluctuation theorem is shown to emerge almost immediately by the mere
application of an inverse Fourier transformation
Escape rates in periodically driven Markov processes
We present an approximate analytical expression for the escape rate of
time-dependent driven stochastic processes with an absorbing boundary such as
the driven leaky integrate-and-fire model for neural spiking. The novel
approximation is based on a discrete state Markovian modeling of the full
long-time dynamics with time-dependent rates. It is valid in a wide parameter
regime beyond the restraining limits of weak driving (linear response) and/or
weak noise. The scheme is carefully tested and yields excellent agreement with
three different numerical methods based on the Langevin equation, the
Fokker-Planck equation and an integral equation.Comment: 10 pages, 5 figure
Rate description of Fokker-Planck processes with time-periodic parameters
The large time dynamics of a periodically driven Fokker-Planck process
possessing several metastable states is investigated. At weak noise transitions
between the metastable states are rare. Their dynamics then represent a
discrete Markovian process characterized by time dependent rates. Apart from
the occupation probabilities, so-called specific probability densities and
localizing functions can be associated to each metastable state. Together,
these three sets of functions uniquely characterize the large time dynamics of
the conditional probability density of the original process. Exact equations of
motion are formulated for these three sets of functions and strategies are
discussed how to solve them. These methods are illustrated and their usefulness
is demonstrated by means of the example of a bistable Brownian oscillator
within a large range of driving frequencies from the slow semiadiabatic to the
fast driving regime
Finite Bath Fluctuation Theorem
We demonstrate that a Finite Bath Fluctuation Theorem of the Crooks type
holds for systems that have been thermalized via weakly coupling it to a bath
with energy independent finite specific heat. We show that this theorem reduces
to the known canonical and microcanonical fluctuation theorems in the two
respective limiting cases of infinite and vanishing specific heat of the bath.
The result is elucidated by applying it to a 2D hard disk colliding elastically
with few other hard disks in a rectangular box with perfectly reflecting walls.Comment: 10 pages, 2 figures. Added Sec. V and App.
Work distributions for random sudden quantum quenches
The statistics of work performed on a system by a sudden random quench is
investigated. Considering systems with finite dimensional Hilbert spaces we
model a sudden random quench by randomly choosing elements from a Gaussian
unitary ensemble (GUE) consisting of hermitean matrices with identically,
Gaussian distributed matrix elements. A probability density function (pdf) of
work in terms of initial and final energy distributions is derived and
evaluated for a two-level system. Explicit results are obtained for quenches
with a sharply given initial Hamiltonian, while the work pdfs for quenches
between Hamiltonians from two independent GUEs can only be determined in
explicit form in the limits of zero and infinite temperature
Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
The quantum version of the Bochkov-Kuzovlev identity is derived on the basis
of the appropriate definition of work as the difference of the measured
internal energies of a quantum system at the beginning and at the end of an
external action on the system given by a prescribed protocol. According to the
spirit of the original Bochkov-Kuzovlev approach, we adopt the "exclusive"
viewpoint, meaning that the coupling to the external work-source is {\it not}
counted as part of the internal energy. The corresponding canonical and
microcanonical quantum fluctuation theorems are derived as well, and are
compared to the respective theorems obtained within the "inclusive" approach.
The relations between the quantum inclusive-work , the exclusive-work
and the dissipated-work , are discussed and clarified. We show by an
explicit example that and are distinct stochastic quantities
obeying different statistics.Comment: 16 page
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
Quantum fluctuation theorems and power measurements
Work in the paradigm of the quantum fluctuation theorems of Crooks and
Jarzynski is determined by projective measurements of energy at the beginning
and end of the force protocol. In analogy to classical systems, we consider an
alternative definition of work given by the integral of the supplied power
determined by integrating up the results of repeated measurements of the
instantaneous power during the force protocol. We observe that such a
definition of work, in spite of taking account of the process dependence, has
different possible values and statistics from the work determined by the
conventional two energy measurement approach (TEMA). In the limit of many
projective measurements of power, the system's dynamics is frozen in the power
measurement basis due to the quantum Zeno effect leading to statistics only
trivially dependent on the force protocol. In general the Jarzynski relation is
not satisfied except for the case when the instantaneous power operator
commutes with the total Hamiltonian at all times. We also consider properties
of the joint statistics of power-based definition of work and TEMA work in
protocols where both values are determined. This allows us to quantify their
correlations. Relaxing the projective measurement condition, weak continuous
measurements of power are considered within the stochastic master equation
formalism. Even in this scenario the power-based work statistics is in general
not able to reproduce qualitative features of the TEMA work statistics.Comment: 26 pages, 9 figure
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