62 research outputs found
Inflow rate, a time-symmetric observable obeying fluctuation relations
While entropy changes are the usual subject of fluctuation theorems, we seek
fluctuation relations involving time-symmetric quantities, namely observables
that do not change sign if the trajectories are observed backward in time. We
find detailed and integral fluctuation relations for the (time integrated)
difference between "entrance rate" and escape rate in mesoscopic jump systems.
Such "inflow rate", which is even under time reversal, represents the
discrete-state equivalent of the phase space contraction rate. Indeed, it
becomes minus the divergence of forces in the continuum limit to overdamped
diffusion. This establishes a formal connection between reversible
deterministic systems and irreversible stochastic ones, confirming that
fluctuation theorems are largely independent of the details of the underling
dynamics.Comment: v3: published version, slightly shorter title and abstrac
Nonequilibrium temperature response for stochastic overdamped systems
The thermal response of nonequilibrium systems requires the knowledge of
concepts that go beyond entropy production. This is showed for systems obeying
overdamped Langevin dynamics, either in steady states or going through a
relaxation process. Namely, we derive the linear response to perturbations of
the noise intensity, mapping it onto the quadratic response to a constant small
force. The latter, displaying divergent terms, is explicitly regularized with a
novel path-integral method. The nonequilibrium equivalents of heat capacity and
thermal expansion coefficient are two applications of this approach, as we show
with numerical examples.Comment: 23 pages, 2 figure
Four out-of-equilibrium lectures
A collection of published papers on the subject of classical nonequilibrium statistical mechanics. Mainly stochastic systems are considered, with special regard to applications in soft matter physic
About the role of chaos and coarse graining in Statistical Mechanics
We discuss the role of ergodicity and chaos for the validity of statistical
laws. In particular we explore the basic aspects of chaotic systems (with
emphasis on the finite-resolution) on systems composed of a huge number of
particles.Comment: Summer school `Fundamental Problems in Statistical Physics' (Leuven,
Belgium), June 16-29, 2013. To be published in Physica
Local detailed balance across scales: from diffusions to jump processes and beyond
Diffusive dynamics in presence of deep energy minima and weak nongradient
forces can be coarse-grained into a mesoscopic jump process over the various
basins of attraction. Combining standard weak-noise results with a path
integral expansion around equilibrium, we show that the emerging transition
rates satisfy local detailed balance (LDB). Namely, the log ratio of the
transition rates between nearby basins of attractions equals the free-energy
variation appearing at equilibrium, supplemented by the work done by the
nonconservative forces along the typical transition path. When the mesoscopic
dynamics possesses a large-size deterministic limit, it can be further reduced
to a jump process over macroscopic states satisfying LDB. The persistence of
LDB under coarse graining of weakly nonequilibrium states is a generic
consequence of the fact that only dissipative effects matter close to
equilibrium.Comment: 8 pages, 3 figure
Macroscopic Stochastic Thermodynamics
Starting at the mesoscopic level with a general formulation of stochastic
thermodynamics in terms of Markov jump processes, we identify the scaling
conditions that ensure the emergence of a (typically nonlinear) deterministic
dynamics and an extensive thermodynamics at the macroscopic level. We then use
large deviations theory to build a macroscopic fluctuation theory around this
deterministic behavior, which we show preserves the fluctuation theorem. For
many systems (e.g. chemical reaction networks, electronic circuits, Potts
models), this theory does not coincide with Langevin-equation approaches
(obtained by adding Gaussian white noise to the deterministic dynamics) which,
if used, are thermodynamically inconsistent. Einstein-Onsager theory of
Gaussian fluctuations and irreversible thermodynamics are recovered at
equilibrium and close to it, respectively. Far from equilibirum, the free
energy is replaced by the dynamically generated quasi-potential (or
self-information) which is a Lyapunov function for the macroscopic dynamics.
Remarkably, thermodynamics connects the dissipation along deterministic and
escape trajectories to the Freidlin-Wentzell quasi-potential, thus constraining
the transition rates between attractors induced by rare fluctuations. A
coherent perspective on minimum and maximum entropy production principles is
also provided. For systems that admit a continuous-space limit, we derive a
nonequilibrium fluctuating field theory with its associated thermodynamics.
Finally, we coarse grain the macroscopic stochastic dynamics into a Markov jump
process describing transitions among deterministic attractors and formulate the
stochastic thermodynamics emerging from it.Comment: Theory part, examples will be added in the following versio
Thermal response of nonequilibrium RC-circuits
We analyze experimental data obtained from an electrical circuit having
components at different temperatures, showing how to predict its response to
temperature variations. This illustrates in detail how to utilize a recent
linear response theory for nonequilibrium overdamped stochastic systems. To
validate these results, we introduce a reweighting procedure that mimics the
actual realization of the perturbation and allows extracting the susceptibility
of the system from steady state data. This procedure is closely related to
other fluctuation-response relations based on the knowledge of the steady state
probability distribution. As an example, we show that the nonequilibrium heat
capacity in general does not correspond to the correlation between the energy
of the system and the heat flowing into it. Rather, also non-dissipative
aspects are relevant in the nonequilbrium fluctuation response relations.Comment: 2 figure
Negative differential response in chemical reactions
Reaction currents in chemical networks usually increase when increasing their
driving affinities. But far from equilibrium the opposite can also happen. We
find that such negative differential response (NDR) occurs in reaction schemes
of major biological relevance, namely, substrate inhibition and autocatalysis.
We do so by deriving the full counting statistics of two minimal representative
models using large deviation methods. We argue that NDR implies the existence
of optimal affinities that maximize the robustness against environmental and
intrinsic noise at intermediate values of dissipation. An analogous behavior is
found in dissipative self-assembly, for which we identify the optimal working
conditions set by NDR.Comment: Main text and S
The dissipation-time uncertainty relation
We show that the dissipation rate bounds the rate at which physical processes
can be performed in stochastic systems far from equilibrium. Namely, for rare
processes we prove the fundamental tradeoff between the entropy flow into the reservoirs and the mean time to
complete a process. This dissipation-time uncertainty relation is a novel form
of speed limit: the smaller the dissipation, the larger the time to perform a
process.Comment: Supplemented by detailed derivation
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