300 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
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.
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
Markovian embedding of non-Markovian superdiffusion
We consider different Markovian embedding schemes of non-Markovian stochastic
processes that are described by generalized Langevin equations (GLE) and obey
thermal detailed balance under equilibrium conditions. At thermal equilibrium
superdiffusive behavior can emerge if the total integral of the memory kernel
vanishes. Such a situation of vanishing static friction is caused by a
super-Ohmic thermal bath. One of the simplest models of ballistic
superdiffusion is determined by a bi-exponential memory kernel that was
proposed by Bao [J.-D. Bao, J. Stat. Phys. 114, 503 (2004)]. We show that this
non-Markovian model has infinitely many different 4-dimensional Markovian
embeddings. Implementing numerically the simplest one, we demonstrate that (i)
the presence of a periodic potential with arbitrarily low barriers changes the
asymptotic large time behavior from free ballistic superdiffusion into normal
diffusion; (ii) an additional biasing force renders the asymptotic dynamics
superdiffusive again. The development of transients that display a
qualitatively different behavior compared to the true large-time asymptotics
presents a general feature of this non-Markovian dynamics. These transients
though may be extremely long. As a consequence, they can be even mistaken as
the true asymptotics. We find that such intermediate asymptotics exhibit a
giant enhancement of superdiffusion in tilted washboard potentials and it is
accompanied by a giant transient superballistic current growing proportional to
with an exponent that can exceed
the ballistic value of two
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
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