13 research outputs found
Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain
In this paper, we present a general derivation of a modified
fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary
state for a system obeying markovian dynamics. We show that the method to
derive modified fluctuation-dissipation theorems near non-equilibrium
stationary states used by J. Prost et al., PRL 103, 090601 (2009), is
generalizable to non-stationary states. This result follows from both standard
linear response theory and from a transient fluctuation theorem, analogous to
the Hatano-Sasa relation. We show that this modified fluctuation-dissipation
theorem can be interpreted at the trajectory level using the notion of
stochastic trajectory entropy, in a way which is similar to what has been done
recently in the case of MFDT near non-equilibrium steady states (NESS). We
illustrate this framework with two solvable examples: the first example
corresponds to a brownian particle in an harmonic trap submitted to a quench of
temperature and to a time-dependent stiffness. The second example is a classic
model of coarsening systems, namely the 1D Ising model with Glauber dynamics.Comment: 25 pages, 4 figure
Heat release by controlled continuous-time Markov jump processes
We derive the equations governing the protocols minimizing the heat released
by a continuous-time Markov jump process on a one-dimensional countable state
space during a transition between assigned initial and final probability
distributions in a finite time horizon. In particular, we identify the
hypotheses on the transition rates under which the optimal control strategy and
the probability distribution of the Markov jump problem obey a system of
differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh
tends to zero, these equations converge to those satisfied by the diffusion
process minimizing the heat released in the Langevin formulation of the same
problem. We also show that in full analogy with the continuum case, heat
minimization is equivalent to entropy production minimization. Thus, our
results may be interpreted as a refined version of the second law of
thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure
Effective bandwidth of non-Markovian packet traffic
We demonstrate the application of recent advances in statistical mechanics to
a problem in telecommunication engineering: the assessment of the quality of a
communication channel in terms of rare and extreme events. In particular, we
discuss non-Markovian models for telecommunication traffic in continuous time
and deploy the "cloning" procedure of non-equilibrium statistical mechanics to
efficiently compute their effective bandwidths. The cloning method allows us to
evaluate the performance of a traffic protocol even in the absence of
analytical results, which are often hard to obtain when the dynamics are
non-Markovian
Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain
In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the method for deriving modified fluctuation-dissipation theorems near non-equilibrium stationary states used by Prost et al (2009 Phys. Rev. Lett. 103 090601) is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano?Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy in a way which is similar to what has been done recently in the case of the MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a Brownian particle in a harmonic trap subjected to a quench of temperature and to a time-dependent stiffness; the second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics
Information thermodynamics for interacting stochastic systems without bipartite structure
36 pages, 4 figuresFluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or information thermodynamics. This means that fluctuations in each subsystem are not independent: subsystems jump simultaneously if the dynamics is modeled as a Markov jump process, or noises are correlated for diffusion processes. In this paper, we consider information and thermodynamic exchanges between a pair of coupled systems that do not satisfy the bipartite property. The generalization of information-theoretic measures, such as learning rates and transfer entropy rates, to this situation is non-trivial and also involves introducing several additional rates. We describe how this can be achieved in the framework of general continuous-time Markov processes, without restricting the study to the steady-state regime. We illustrate our general formalism on the case of diffusion processes and derive an extension of the second law of information thermodynamics in which the difference of transfer entropy rates in the forward and backward time directions replaces the learning rate. As a side result, we also generalize an important relation linking information theory and estimation theory. To further obtain analytical expressions we treat in detail the case of Ornstein-Uhlenbeck processes, and discuss the ability of the various information measures to detect a directional coupling in the presence of correlated noises. Finally, we apply our formalism to the analysis of the directional influence between cellular processes in a concrete example, which also requires considering the case of a non-bipartite and non-Markovian process