287 research outputs found
Quantum work relations and response theory
A universal quantum work relation is proved for isolated time-dependent
Hamiltonian systems in a magnetic field as the consequence of
microreversibility. This relation involves a functional of an arbitrary
observable. The quantum Jarzynski equality is recovered in the case this
observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity
relations are deduced thereof in the linear response regime
Geometric magnetism in open quantum systems
An isolated classical chaotic system, when driven by the slow change of
several parameters, responds with two reaction forces: geometric friction and
geometric magnetism. By using the theory of quantum fluctuation relations we
show that this holds true also for open quantum systems, and provide explicit
expressions for those forces in this case. This extends the concept of Berry
curvature to the realm of open quantum systems. We illustrate our findings by
calculating the geometric magnetism of a damped charged quantum harmonic
oscillator transported along a path in physical space in presence of a magnetic
field and a thermal environment. We find that in this case the geometric
magnetism is unaffected by the presence of the heat bath.Comment: 7 pages. Signs corrected. v3 Accepted in Phys. Rev.
Symmetry Relations for Trajectories of a Brownian Motor
A Brownian Motor is a nanoscale or molecular device that combines the effects
of thermal noise, spatial or temporal asymmetry, and directionless input energy
to drive directed motion. Because of the input energy, Brownian motors function
away from thermodynamic equilibrium and concepts such as linear response
theory, fluctuation dissipation relations, and detailed balance do not apply.
The {\em generalized} fluctuation-dissipation relation, however, states that
even under strongly thermodynamically non-equilibrium conditions the ratio of
the probability of a transition to the probability of the time-reverse of that
transition is the exponent of the change in the internal energy of the system
due to the transition. Here, we derive an extension of the generalized
fluctuation dissipation theorem for a Brownian motor for the ratio between the
probability for the motor to take a forward step and the probability to take a
backward step
Comparison of work fluctuation relations
We compare two predictions regarding the microscopic fluctuations of a system
that is driven away from equilibrium: one due to Crooks [J. Stat. Phys. 90,
1481 (1998)] which has gained recent attention in the context of nonequilibrium
work and fluctuation theorems, and an earlier, analogous result obtained by
Bochkov and Kuzovlev [Zh. Eksp. Teor. Fiz. 72(1), 238247 (1977)]. Both results
quantify irreversible behavior by comparing probabilities of observing
particular microscopic trajectories during thermodynamic processes related by
time-reversal, and both are expressed in terms of the work performed when
driving the system away from equilibrium. By deriving these two predictions
within a single, Hamiltonian framework, we clarify the precise relationship
between them, and discuss how the different definitions of work used by the two
sets of authors gives rise to different physical interpretations. We then
obtain a extended fluctuation relation that contains both the Crooks and the
Bochkov-Kuzovlev results as special cases.Comment: 14 pages with 1 figure, accepted for publication in the Journal of
Statistical Mechanic
Lower bounds on dissipation upon coarse graining
By different coarse-graining procedures we derive lower bounds on the total
mean work dissipated in Brownian systems driven out of equilibrium. With
several analytically solvable examples we illustrate how, when, and where the
information on the dissipation is captured.Comment: 11 pages, 8 figure
Work extraction in the spin-boson model
We show that work can be extracted from a two-level system (spin) coupled to
a bosonic thermal bath. This is possible due to different initial temperatures
of the spin and the bath, both positive (no spin population inversion) and is
realized by means of a suitable sequence of sharp pulses applied to the spin.
The extracted work can be of the order of the response energy of the bath,
therefore much larger than the energy of the spin. Moreover, the efficiency of
extraction can be very close to its maximum, given by the Carnot bound, at the
same time the overall amount of the extracted work is maximal. Therefore, we
get a finite power at efficiency close to the Carnot bound.
The effect comes from the backreaction of the spin on the bath, and it
survives for a strongly disordered (inhomogeneously broadened) ensemble of
spins. It is connected with generation of coherences during the work-extraction
process, and we derived it in an exactly solvable model. All the necessary
general thermodynamical relations are derived from the first principles of
quantum mechanics and connections are made with processes of lasing without
inversion and with quantum heat engines.Comment: 30 pages, 6 figure
Random paths and current fluctuations in nonequilibrium statistical mechanics
An overview is given of recent advances in nonequilibrium statistical
mechanics about the statistics of random paths and current fluctuations.
Although statistics is carried out in space for equilibrium statistical
mechanics, statistics is considered in time or spacetime for nonequilibrium
systems. In this approach, relationships have been established between
nonequilibrium properties such as the transport coefficients, the thermodynamic
entropy production, or the affinities, and quantities characterizing the
microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate.
This overview presents results for classical systems in the escape-rate
formalism, stochastic processes, and open quantum systems
Non-equilibrium work relations
This is a brief review of recently derived relations describing the behaviour
of systems far from equilibrium. They include the Fluctuation Theorem,
Jarzynski's and Crooks' equalities, and an extended form of the Second
Principle for general steady states. They are very general and their proofs
are, in most cases, disconcertingly simple.Comment: Brief Summer School Lecture Note
Fluctuation theorems and atypical trajectories
In this work, we have studied simple models that can be solved analytically
to illustrate various fluctuation theorems. These fluctuation theorems provide
symmetries individually to the distributions of physical quantities like the
classical work (), thermodynamic work (), total entropy () and dissipated heat (), when the system is driven arbitrarily out
of equilibrium. All these quantities can be defined for individual
trajectories. We have studied the number of trajectories which exhibit
behaviour unexpected at the macroscopic level. As the time of observation
increases, the fraction of such atypical trajectories decreases, as expected at
macroscale. Nature of distributions for the thermodynamic work and the entropy
production in nonlinear models may exhibit peak (most probable value) in the
atypical regime without violating the expected average behaviour. However,
dissipated heat and classical work exhibit peak in the regime of typical
behaviour only.Comment: 14 pages, 7 figure
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