7,687 research outputs found
General no-go condition for stochastic pumping
The control of chemical dynamics requires understanding the effect of
time-dependent transition rates between states of chemo-mechanical molecular
configurations. Pumping refers to generating a net current, e.g. per period in
the time-dependence, through a cycle of consecutive states. The working of
artificial machines or synthesized molecular motors depends on it. In this
paper we give short and simple proofs of no-go theorems, some of which appeared
before but here with essential extensions to non-Markovian dynamics, including
the study of the diffusion limit. It allows to exclude certain protocols in the
working of chemical motors where only the depth of the energy well is changed
in time and not the barrier height between pairs of states. We also show how
pre-existing steady state currents are in general modified with a
multiplicative factor when this time-dependence is turned on.Comment: 8 pages; v2: minor changes, 1 reference adde
A nonequilibrium extension of the Clausius heat theorem
We generalize the Clausius (in)equality to overdamped mesoscopic and
macroscopic diffusions in the presence of nonconservative forces. In contrast
to previous frameworks, we use a decomposition scheme for heat which is based
on an exact variant of the Minimum Entropy Production Principle as obtained
from dynamical fluctuation theory. This new extended heat theorem holds true
for arbitrary driving and does not require assumptions of local or close to
equilibrium. The argument remains exactly intact for diffusing fields where the
fields correspond to macroscopic profiles of interacting particles under
hydrodynamic fluctuations. We also show that the change of Shannon entropy is
related to the antisymmetric part under a modified time-reversal of the
time-integrated entropy flux.Comment: 23 pages; v2: manuscript significantly extende
Time-symmetric fluctuations in nonequilibrium systems
For nonequilibrium steady states, we identify observables whose fluctuations
satisfy a general symmetry and for which a new reciprocity relation can be
shown. Unlike the situation in recently discussed fluctuation theorems, these
observables are time-reversal symmetric. That is essential for exploiting the
fluctuation symmetry beyond linear response theory. Besides time-reversal, a
crucial role is played by the reversal of the driving fields, that further
resolves the space-time action. In particular, the time-symmetric part in the
space-time action determines second order effects of the nonequilibrium
driving.Comment: 4 page
On the validity of entropy production principles for linear electrical circuits
We discuss the validity of close-to-equilibrium entropy production principles
in the context of linear electrical circuits. Both the minimum and the maximum
entropy production principle are understood within dynamical fluctuation
theory. The starting point are Langevin equations obtained by combining
Kirchoff's laws with a Johnson-Nyquist noise at each dissipative element in the
circuit. The main observation is that the fluctuation functional for time
averages, that can be read off from the path-space action, is in first order
around equilibrium given by an entropy production rate. That allows to
understand beyond the schemes of irreversible thermodynamics (1) the validity
of the least dissipation, the minimum entropy production, and the maximum
entropy production principles close to equilibrium; (2) the role of the
observables' parity under time-reversal and, in particular, the origin of
Landauer's counterexample (1975) from the fact that the fluctuating observable
there is odd under time-reversal; (3) the critical remark of Jaynes (1980)
concerning the apparent inappropriateness of entropy production principles in
temperature-inhomogeneous circuits.Comment: 19 pages, 1 fi
Heat bounds and the blowtorch theorem
We study driven systems with possible population inversion and we give
optimal bounds on the relative occupations in terms of released heat. A precise
meaning to Landauer's blowtorch theorem (1975) is obtained stating that
nonequilibrium occupations are essentially modified by kinetic effects. Towards
very low temperatures we apply a Freidlin-Wentzel type analysis for continuous
time Markov jump processes. It leads to a definition of dominant states in
terms of both heat and escape rates.Comment: 11 pages; v2: minor changes, 1 reference adde
Enstrophy dissipation in two-dimensional turbulence
Insight into the problem of two-dimensional turbulence can be obtained by an
analogy with a heat conduction network. It allows the identification of an
entropy function associated to the enstrophy dissipation and that fluctuates
around a positive (mean) value. While the corresponding enstrophy network is
highly nonlocal, the direction of the enstrophy current follows from the Second
Law of Thermodynamics. An essential parameter is the ratio of the intensity of driving as a function of
wavenumber , to the dissipation strength , where is the
viscosity. The enstrophy current flows from higher to lower values of ,
similar to a heat current from higher to lower temperature. Our probabilistic
analysis of the enstrophy dissipation and the analogy with heat conduction thus
complements and visualizes the more traditional spectral arguments for the
direct enstrophy cascade. We also show a fluctuation symmetry in the
distribution of the total entropy production which relates the probabilities of
direct and inverse enstrophy cascades.Comment: 8 pages, revtex
Dynamical fluctuations for semi-Markov processes
We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov
processes. Our main result is an exact large time asymptotics for the joint
probability of the occupation times and the currents in the system,
establishing some generic large deviation structures. We discuss in detail how
the nonequilibrium driving and the non-exponential waiting time distribution
influence the occupation-current statistics. The violation of the Markov
condition is reflected in the emergence of a new type of nonlocality in the
fluctuations. Explicit solutions are obtained for some examples of driven
random walks on the ring.Comment: Minor changes, accepted for publication in Journal of Physics
Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics
We continue our study of the linear response of a nonequilibrium system. This
Part II concentrates on models of open and driven inertial dynamics but the
structure and the interpretation of the result remain unchanged: the response
can be expressed as a sum of two temporal correlations in the unperturbed
system, one entropic, the other frenetic. The decomposition arises from the
(anti)symmetry under time-reversal on the level of the nonequilibrium action.
The response formula involves a statistical averaging over explicitly known
observables but, in contrast with the equilibrium situation, they depend on the
model dynamics in terms of an excess in dynamical activity. As an example, the
Einstein relation between mobility and diffusion constant is modified by a
correlation term between the position and the momentum of the particle
The Measure-theoretic Identity Underlying Transient Fluctuation Theorems
We prove a measure-theoretic identity that underlies all transient
fluctuation theorems (TFTs) for entropy production and dissipated work in
inhomogeneous deterministic and stochastic processes, including those of Evans
and Searles, Crooks, and Seifert. The identity is used to deduce a tautological
physical interpretation of TFTs in terms of the arrow of time, and its
generality reveals that the self-inverse nature of the various trajectory and
process transformations historically relied upon to prove TFTs, while necessary
for these theorems from a physical standpoint, is not necessary from a
mathematical one. The moment generating functions of thermodynamic variables
appearing in the identity are shown to converge in general only in a vertical
strip in the complex plane, with the consequence that a TFT that holds over
arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem
for any possible speed of the corresponding large deviation principle. The case
of strongly biased birth-death chains is presented to illustrate this
phenomenon. We also discuss insights obtained from our measure-theoretic
formalism into the results of Saha et. al. on the breakdown of TFTs for driven
Brownian particles
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