85,215 research outputs found
Posterior probability and fluctuation theorem in stochastic processes
A generalization of fluctuation theorems in stochastic processes is proposed.
The new theorem is written in terms of posterior probabilities, which are
introduced via the Bayes theorem. In usual fluctuation theorems, a forward path
and its time reversal play an important role, so that a microscopically
reversible condition is essential. In contrast, the microscopically reversible
condition is not necessary in the new theorem. It is shown that the new theorem
adequately recovers various theorems and relations previously known, such as
the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the
Hatano-Sasa relation, when adequate assumptions are employed.Comment: 4 page
A local fluctuation theorem for large systems
The fluctuation theorem characterizes the distribution of the dissipation in
nonequilibrium systems and proves that the average dissipation will be
positive. For a large system with no external source of fluctuation,
fluctuations in properties will become unobservable and details of the
fluctuation theorem are unable to be explored. In this letter, we consider such
a situation and show how a fluctuation theorem can be obtained for a small open
subsystem within the large system. We find that a correction term has to be
added to the large system fluctuation theorem due to correlation of the
subsystem with the surroundings. Its analytic expression can be derived
provided some general assumptions are fulfilled, and its relevance it checked
using numerical simulations.Comment: 5 pages, 5 figures; revised and supplementary material include
Fluctuation theorems for excess and housekeeping heats for underdamped systems
We present a simple derivation of the integral fluctuation theorems for
excess housekeeping heat for an underdamped Langevin system, without using the
concept of dual dynamics. In conformity with the earlier results, we find that
the fluctuation theorem for housekeeping heat holds when the steady state
distributions are symmetric in velocity, whereas there is no such requirement
for the excess heat. We first prove the integral fluctuation theorem for the
excess heat, and then show that it naturally leads to the integral fluctuation
theorem for housekeeping heat. We also derive the modified detailed fluctuation
theorems for the excess and housekeeping heats.Comment: 10 pages. Section 3 contains further generalization
Unified Treatment of Quantum Fluctuation Theorem and Jarzynski Equality in Terms of microscopic reversibility
There are two related theorems which hold even in far from equilibrium,
namely fluctuation theorem and Jarzynski equality. Fluctuation theorem states
the existence of symmetry of fluctuation of entropy production, while Jarzynski
equality enables us to estimate the free energy change between two states by
using irreversible processes. On the other hand, relationship between these
theorems was investigated by Crooks for the classical stochastic systems. In
this letter, we derive quantum analogues of fluctuation theorem and Jarzynski
equality microscopic reversibility condition. In other words, the quantum
analogue of the work by Crooks is presented.Comment: 7pages, revised versio
A local fluctuation theorem
A mechanism for the validity of a local version of the fluctuation theorem,
uniform in the system size, is discussed for a reversible chain of weakly
coupled Anosov systems.Comment: plain TeX, 1 figur
Fluctuation Theorem and Chaos
The heat theorem (i.e. the second law of thermodynamics or the existence of
entropy) is a manifestation of a general property of hamiltonian mechanics and
of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary
states the chaotic hypothesis plays a similar role: it allows a unique
determination of the probability distribution (called {\rm SRB} distribution on
phase space providing the time averages of the observables. It also implies an
expression for a few averages concrete enough to derive consequences of
symmetry properties like the fluctuation theorem or to formulate a theory of
coarse graining unifying the foundations of equilibrium and of nonequilibrium.Comment: Basis for the plenary talk at StatPhys23 (Genova July 2007
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.
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