142 research outputs found
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
The Steady State Distribution of the Master Equation
The steady states of the master equation are investigated. We give two
expressions for the steady state distribution of the master equation a la the
Zubarev-McLennan steady state distribution, i.e., the exact expression and an
expression near equilibrium. The latter expression obtained is consistent with
recent attempt of constructing steady state theormodynamics.Comment: 6 pages, No figures. A mistake was correcte
Noncyclic and nonadiabatic geometric phase for counting statistics
We propose a general framework of the geometric-phase interpretation for
counting statistics. Counting statistics is a scheme to count the number of
specific transitions in a stochastic process. The cumulant generating function
for the counting statistics can be interpreted as a `phase', and it is
generally divided into two parts: the dynamical phase and a remaining one. It
has already been shown that for cyclic evolution the remaining phase
corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan
phase. We here show that the remaining phase also has an interpretation as a
geometric phase even in noncyclic and nonadiabatic evolution.Comment: 12 pages, 1 figur
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 for harmonic oscillators
We study experimentally the thermal fluctuations of energy input and
dissipation in a harmonic oscillator driven out of equilibrium, and search for
Fluctuation Relations. We study transient evolution from the equilibrium state,
together with non equilibrium steady states. Fluctuations Relations are
obtained experimentally for both the work and the heat, for the stationary and
transient evolutions. A Stationary State Fluctuation Theorem is verified for
the two time prescriptions of the torque. But a Transient Fluctuation Theorem
is satisfied for the work given to the system but not for the heat dissipated
by the system in the case of linear forcing. Experimental observations on the
statistical and dynamical properties of the fluctuation of the angle, we derive
analytical expressions for the probability density function of the work and the
heat. We obtain for the first time an analytic expression of the probability
density function of the heat. Agreement between experiments and our modeling is
excellent
Path-integral analysis of fluctuation theorems for general Langevin processes
We examine classical, transient fluctuation theorems within the unifying
framework of Langevin dynamics. We explicitly distinguish between the effects
of non-conservative forces that violate detailed balance, and non-autonomous
dynamics arising from the variation of an external parameter. When both these
sources of nonequilibrium behavior are present, there naturally arise two
distinct fluctuation theorems.Comment: 24 pages, one figur
Fluctuation theorems for stochastic dynamics
Fluctuation theorems make use of time reversal to make predictions about
entropy production in many-body systems far from thermal equilibrium. Here we
review the wide variety of distinct, but interconnected, relations that have
been derived and investigated theoretically and experimentally. Significantly,
we demonstrate, in the context of Markovian stochastic dynamics, how these
different fluctuation theorems arise from a simple fundamental time-reversal
symmetry of a certain class of observables. Appealing to the notion of Gibbs
entropy allows for a microscopic definition of entropy production in terms of
these observables. We work with the master equation approach, which leads to a
mathematically straightforward proof and provides direct insight into the
probabilistic meaning of the quantities involved. Finally, we point to some
experiments that elucidate the practical significance of fluctuation relations.Comment: 48 pages, 2 figures. v2: minor changes for consistency with published
versio
Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
We study first-order quantum phase transitions in models where the mean-field
traitment is exact, and the exponentially fast closure of the energy gap with
the system size at the transition. We consider exactly solvable ferromagnetic
models, and show that they reduce to the Grover problem in a particular limit.
We compute the coefficient in the exponential closure of the gap using an
instantonic approach, and discuss the (dire) consequences for quantum
annealing.Comment: 6 pages, 3 figure
Fluctuation relations and coarse-graining
We consider the application of fluctuation relations to the dynamics of
coarse-grained systems, as might arise in a hypothetical experiment in which a
system is monitored with a low-resolution measuring apparatus. We analyze a
stochastic, Markovian jump process with a specific structure that lends itself
naturally to coarse-graining. A perturbative analysis yields a reduced
stochastic jump process that approximates the coarse-grained dynamics of the
original system. This leads to a non-trivial fluctuation relation that is
approximately satisfied by the coarse-grained dynamics. We illustrate our
results by computing the large deviations of a particular stochastic jump
process. Our results highlight the possibility that observed deviations from
fluctuation relations might be due to the presence of unobserved degrees of
freedom.Comment: 19 pages, 6 figures, very minor change
Stick-slip motion of solids with dry friction subject to random vibrations and an external field
We investigate a model for the dynamics of a solid object, which moves over a
randomly vibrating solid surface and is subject to a constant external force.
The dry friction between the two solids is modeled phenomenologically as being
proportional to the sign of the object's velocity relative to the surface, and
therefore shows a discontinuity at zero velocity. Using a path integral
approach, we derive analytical expressions for the transition probability of
the object's velocity and the stationary distribution of the work done on the
object due to the external force. From the latter distribution, we also derive
a fluctuation relation for the mechanical work fluctuations, which incorporates
the effect of the dry friction.Comment: v1: 23 pages, 9 figures; v2: Reference list corrected; v3: Published
version, typos corrected, references adde
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