34 research outputs found
Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
We derive general bounds on the probability that the empirical first-passage
time of a reversible ergodic
Markov process inferred from a sample of independent realizations deviates
from the true mean first-passage time by more than any given amount in either
direction. We construct non-asymptotic confidence intervals that hold in the
elusive small-sample regime and thus fill the gap between asymptotic methods
and the Bayesian approach that is known to be sensitive to prior belief and
tends to underestimate uncertainty in the small-sample setting. Our
concentration-of-measure-based results allow for model-free error control and
reliable error estimation in kinetic inference, and are thus important for the
analysis of experimental and simulation data in the presence of limited
sampling
Comment on "Inferring broken detailed balance in the absence of observable currents"
We present a simple biophysical example that invalidates the main conclusion
of "Nat. Commun. 10, 3542 (2019)". Moreover, we explain that systems with one
or more hidden states between at least one pair of observed states that give
rise to non-instantaneous transition paths between these states also invalidate
the main conclusion of the aforementioned work. This provides a flexible
roadmap for constructing counterexamples. We hope for this comment to raise
awareness of possibly hidden transition paths and of the importance of
considering the microscopic origin of emerging non-Markovian (or Markovian)
dynamics for thermodynamics.Comment: 3 pages, 1 Figure; submitted to Nature Communications; one reference
removed; some sentences reformulate
Emergent memory and kinetic hysteresis in strongly driven networks
Stochastic network-dynamics are typically assumed to be memory-less.
Involving prolonged dwells interrupted by instantaneous transitions between
nodes such Markov networks stand as a coarse-graining paradigm for chemical
reactions, gene expression, molecular machines, spreading of diseases, protein
dynamics, diffusion in energy landscapes, epigenetics and many others. However,
as soon as transitions cease to be negligibly short, as often observed in
experiments, the dynamics develops a memory. That is, state-changes depend not
only on the present state but also on the past. Here, we establish the first
thermodynamically consistent -- dissipation-preserving -- mapping of continuous
dynamics onto a network, which reveals ingrained dynamical symmetries and an
unforeseen kinetic hysteresis. These symmetries impose three independent
sources of fluctuations in state-to state kinetics that determine the `flavor
of memory'. The hysteresis between the forward/backward in time coarse-graining
of continuous trajectories implies a new paradigm for the thermodynamics of
active molecular processes in the presence of memory, that is, beyond the
assumption of local detailed balance. Our results provide a new understanding
of fluctuations in the operation of molecular machines as well as catch-bonds
involved in cellular adhesion.Comment: 49 pages, 23 figures (main text 15 pages; Appendices 23 pages; SM 11
pages); old Appendices D-F became new Supplementary material, version
accepted in Phys. Rev.
Emergent memory and kinetic hysteresis in strongly driven networks
Stochastic network-dynamics are typically assumed to be memory-less.
Involving prolonged dwells interrupted by instantaneous transitions between
nodes such Markov networks stand as a coarse-graining paradigm for chemical
reactions, gene expression, molecular machines, spreading of diseases, protein
dynamics, diffusion in energy landscapes, epigenetics and many others. However,
as soon as transitions cease to be negligibly short, as often observed in
experiments, the dynamics develops a memory. That is, state-changes depend not
only on the present state but also on the past. Here, we establish the first
thermodynamically consistent -- dissipation-preserving -- mapping of continuous
dynamics onto a network, which reveals ingrained dynamical symmetries and an
unforeseen kinetic hysteresis. These symmetries impose three independent
sources of fluctuations in state-to state kinetics that determine the `flavor
of memory'. The hysteresis between the forward/backward in time coarse-graining
of continuous trajectories implies a new paradigm for the thermodynamics of
active molecular processes in the presence of memory, that is, beyond the
assumption of local detailed balance. Our results provide a new understanding
of fluctuations in the operation of molecular machines as well as catch-bonds
involved in cellular adhesion.Comment: 49 pages, 23 figures (main text 15 pages; Appendices 23 pages; SM 11
pages); old Appendices D-F became new Supplementary material, version
accepted in Phys. Rev.
Global Speed Limit for Finite-Time Dynamical Phase Transition and Nonequilibrium Relaxation
Recent works unraveled an intriguing finite-time dynamical phase transition
in the thermal relaxation of the mean field Curie-Weiss model. The phase
transition reflects a sudden switch in the dynamics. Its existence in systems
with a finite range of interaction, however, remained unclear. Here we
demonstrate the dynamical phase transition for nearest-neighbor Ising systems
on the square and Bethe lattices through extensive computer simulations and by
analytical results. Combining large-deviation techniques and Bethe-Guggenheim
theory we prove the existence of the dynamical phase transition for arbitrary
quenches, including those within the two-phase region. Strikingly, for any
given initial condition we prove and explain the existence of non-trivial speed
limits for the dynamical phase transition and the relaxation of magnetization,
which are fully corroborated by simulations of the microscopic Ising model but
are absent in the mean field setting. Pair correlations, which are neglected in
mean field theory and trivial in the Curie-Weiss model, account for kinetic
constraints due to frustrated local configurations that give rise to a global
speed limit
Feynman-Kac theory of time-integrated functionals: It\^o versus functional calculus
The fluctuations of dynamical functionals such as the empirical density and
current as well as heat, work and generalized currents in stochastic
thermodynamics are usually studied within the Feynman-Kac tilting formalism,
which in the Physics literature is typically derived by some form of
Kramers-Moyal expansion, or in the Mathematical literature via the
Cameron-Martin-Girsanov approach. Here we derive the Feynman-Kac theory for
general additive dynamical functionals directly via It\^o calculus and via
functional calculus, where the latter result in fact appears to be new. Using
Dyson series we then independently recapitulate recent results on steady-state
(co)variances of general additive dynamical functionals derived recently in
Dieball and Godec ({2022 \textit{Phys. Rev. Lett.}~\textbf{129} 140601}) and
Dieball and Godec ({2022 \textit{Phys. Rev. Res.}~\textbf{4} 033243}). We hope
for our work to put the different approaches to the statistics of dynamical
functionals employed in the field on a common footing, and to illustrate more
easily accessible ways to the tilting formalism
Faster uphill relaxation in thermodynamically equidistant temperature quenches
We uncover an unforeseen asymmetry in relaxation -- for a pair of
thermodynamically equidistant temperature quenches, one from a lower and the
other from a higher temperature, the relaxation at the ambient temperature is
faster in case of the former. We demonstrate this finding on hand of two
exactly solvable many-body systems relevant in the context of single-molecule
and tracer-particle dynamics. We prove that near stable minima and for all
quadratic energy landscapes it is a general phenomenon that also exists in a
class of non-Markovian observables probed in single-molecule and
particle-tracking experiments. The asymmetry is a general feature of reversible
overdamped diffusive systems with smooth single-well potentials and occurs in
multi-well landscapes when quenches disturb predominantly intra-well
equilibria. Our findings may be relevant for the optimization of stochastic
heat engines.Comment: version accepted in Phys. Rev. Lett.; a couple of typos in the
Supplementary Material are correcte