448 research outputs found
Exact Nonequilibrium Work Generating Function for a Small Classical System
We obtain the exact nonequilibrium work generating function (NEWGF), for a
small system consisting of a massive Brownian particle connected to internal
and external springs. The external work is provided to the system for a finite
time interval. The Jarzynski equality (JE), obtained in this case directly from
the NEWGF, is shown to be valid for the present model, in an exact way
regardless of the rate of external work
Thermodynamics as a nonequilibrium path integral
Thermodynamics is a well developed tool to study systems in equilibrium but
no such general framework is available for non-equilibrium processes. Only hope
for a quantitative description is to fall back upon the equilibrium language as
often done in biology. This gap is bridged by the work theorem. By using this
theorem we show that the Barkhausen-type non-equilibrium noise in a process,
repeated many times, can be combined to construct a special matrix
whose principal eigenvector provides the equilibrium distribution. For an
interacting system , and hence the equilibrium distribution, can be
obtained from the free case without any requirement of equilibrium.Comment: 15 pages, 5 eps files. Final version to appear in J Phys.
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
Molecular random walks and invariance group of the Bogolyubov equation
Statistics of molecular random walks in a fluid is considered with the help
of the Bogolyubov equation for generating functional of distribution functions.
An invariance group of solutions to this equation as functions of the fluid
density is discovered. It results in many exact relations between probability
distribution of the path of a test particle and its irreducible correlations
with the fluid. As the consequence, significant restrictions do arise on
possible shapes of the path distribution. In particular, the hypothetical
Gaussian form of its long-range asymptotic proves to be forbidden (even in the
Boltzmann-Grad limit). Instead, a diffusive asymptotic is allowed which
possesses power-law long tail (cut off by ballistic flight length).Comment: 23 pages, no figures, LaTeX AMSART, author's translation from Russian
of the paper accepted to the TMPh (``Theoretical and mathematical physics''
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
Exponential peak and scaling of work fluctuations in modulated systems
We extend the stationary-state work fluctuation theorem to periodically
modulated nonlinear systems. Such systems often have coexisting stable periodic
states. We show that work fluctuations sharply increase near a kinetic phase
transition where the state populations are close to each other. The work
variance is proportional here to the reciprocal rate of interstate switching.
We also show that the variance displays scaling with the distance to a
bifurcation point and find the critical exponent for a saddle-node bifurcation
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
Thermal Diffusion of a Two Layer System
In this paper thermal conductivity and thermal diffusivity of a two layer
system is examined from the theoretical point of view. We use the one
dimensional heat diffusion equation with the appropriate solution in each layer
and boundary conditions at the interfaces to calculate the heat transport in
this bounded system. We also consider the heat flux at the surface of the samle
as boundary condition instead of using a fixed tempertaure. From this, we
obtain an expression for the efective thermal diffusivity of the composite
sample in terms of the thermal diffusivity of its constituent materials
whithout any approximations.Comment: 16 pages, 1 figure, RevTeX v. 3.0 macro packag
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