161 research outputs found
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.
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''
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
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
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
Minimal Work Principle and its Limits for Classical Systems
The minimal work principle asserts that work done on a thermally isolated
equilibrium system, is minimal for the slowest (adiabatic) realization of a
given process. This principle, one of the formulations of the second law, is
operationally well-defined for any finite (few particle) Hamiltonian system.
Within classical Hamiltonian mechanics, we show that the principle is valid for
a system of which the observable of work is an ergodic function. For
non-ergodic systems the principle may or may not hold, depending on additional
conditions. Examples displaying the limits of the principle are presented and
their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte
Stochastic deformation of a thermodynamic symplectic structure
A stochastic deformation of a thermodynamic symplectic structure is studied.
The stochastic deformation procedure is analogous to the deformation of an
algebra of observables like deformation quantization, but for an imaginary
deformation parameter (the Planck constant). Gauge symmetries of thermodynamics
and corresponding stochastic mechanics, which describes fluctuations of a
thermodynamic system, are revealed and gauge fields are introduced. A physical
interpretation to the gauge transformations and gauge fields is given. An
application of the formalism to a description of systems with distributed
parameters in a local thermodynamic equilibrium is considered.Comment: 22 pages, revtex preprint style; some notations changed and
references added; some formulas and comments adde
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