Feedback cooling, measurement errors, and entropy production

The efficiency of a feedback mechanism depends on the precision of the measurement outcomes obtained from the controlled system. Accordingly, measurement errors affect the entropy production in the system. We explore this issue in the context of active feedback cooling by modeling a typical cold damping setup as a harmonic oscillator in contact with a heat reservoir and submitted to a velocity-dependent feedback force that reduces the random motion. We consider two models that distinguish whether the sensor continuously measures the position of the resonator or directly its velocity (in practice, an electric current). Adopting the standpoint of the controlled system, we identify the `entropy pumping' contribution that describes the entropy reduction due to the feedback control and that modifies the second law of thermodynamics. We also assign a relaxation dynamics to the feedback mechanism and compare the apparent entropy production in the system and the heat bath to the total entropy production in the super-system that includes the controller. In this context, entropy pumping reflects the existence of hidden degrees of freedom and the apparent entropy production satisfies fluctuation theorems associated to an effective Langevin dynamics.Comment: 27 pages, 3 figures. Added references and foonotes. Revised discussion at the end of section 4. Results unchanged. To appear in J. Stat. Mec

Comment on Thermodynamic uncertainty relation for time-delayed Langevin systems

An extension of the thermodynamic uncertainty relation (TUR) to time-delayed Langevin systems has been recently proposed by T. V. Vu and Y. Hasegawa (arXiv:1809.06610v2). Here we show that the derivation is erroneous.Comment: 2 pages, 1 figur

Stochastic dynamics of N bistable elements with global time-delayed interactions: towards an exact solution of the master equations for finite N

We consider a network of N noisy bistable elements with global time-delayed couplings. In a two-state description, where elements are represented by Ising spins, the collective dynamics is described by an infinite hierarchy of coupled master equations which was solved at the mean-field level in the thermodynamic limit. For a finite number of elements, an analytical description was deemed so far intractable and numerical studies seemed to be necessary. In this paper we consider the case of two interacting elements and show that a partial analytical description of the stationary state is possible if the stochastic process is time-symmetric. This requires some relationship between the transition rates to be satisfied.Comment: 17 pages, 7 figure

A self-consistent Ornstein-Zernike approximation for the Random Field Ising model

We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field as an annealed spin variable, thereby avoiding the usual average over the random field distribution. This allows to study the influence of the distribution on the phase diagram in finite dimensions. The thermodynamics and the correlation functions are obtained as solutions of a set a coupled partial differential equations with magnetization, temperature and disorder strength as independent variables. A preliminary analysis based on high-temperature and 1/d series expansions shows that the theory can predict accurately the dependence of the critical temperature on disorder strength for dimensions d>4. For the bimodal distribution, we find a tricritical point which moves to weaker fields as the dimension is reduced. For the Gaussian distribution, a tricritical point may appear for d slightly above 4.Comment: 29 pages, Revtex file, 2 figures included, submitted to `Phys. Rev. B

The ferromagnetic q-state Potts model on three-dimensional lattices: a study for real values of q

We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike approximation for the two-point correlation functions. We calculate the transition temperatures and, when the transition is first order, the jump discontinuities in the magnetization and the internal energy, as well as the coordinates of the critical endpoint in external field. Our predictions are in very good agreement with best available estimates. From the numerical study of the region of weak first-order transition, we estimate the critical value $q_c$ for which the transition changes from second to first-order. The $q->1$ limit that describes the bond-percolation problem is also investigated.Comment: 25 pages,3 tables,8 figure

A self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin glass model

We propose a self-consistent Ornstein-Zernike approximation for studying the Edwards-Anderson spin glass model. By performing two Legendre transforms in replica space, we introduce a Gibbs free energy depending on both the magnetizations and the overlap order parameters. The correlation functions and the thermodynamics are then obtained from the solution of a set of coupled partial differential equations. The approximation becomes exact in the limit of infinite dimension and it provides a potential route for studying the stability of the high-temperature phase against replica-symmetry breaking fluctuations in finite dimensions. As a first step, we present the numerical predictions for the freezing temperature and the zero-field thermodynamic properties above freezing as a function of dimensionality.Comment: 19 pages, 1 figure. submitted to J. Stat. Phy

Numerical study of metastable states in the T=0 RFIM

We study numerically the number of single-spin-flip stable states in the T=0 Random Field Ising Model (RFIM) on random regular graphs of connectivity $z=2$ and $z=4$ and on the cubic lattice. The annealed and quenched complexities (i.e. the entropy densities) of the metastable states with given magnetization are calculated as a function of the external magnetic field. The results show that the appearance of a (disorder-induced) out-of-equilibrium phase transition in the magnetization hysteresis loop at low disorder can be ascribed to a change in the distribution of the metastable states in the field-magnetization plane.Comment: 15 pages, 19 figure

Information thermodynamics for interacting stochastic systems without bipartite structure

Fluctuations 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.Comment: 39 pages, 5 figures. Final version, to appear in J. Stat.Mec

Spontaneous imbibition in disordered porous solids: a theoretical study of helium in silica aerogels

We present a theoretical study of spontaneous imbibition of liquid 4He in silica aerogels focusing on the effect of porosity on the fluid dynamical behavior. We adopt a coarse-grained three-dimensional lattice-gas description like in previous studies of gas adsorption and capillary condensation, and use a dynamical mean-field theory, assuming that capillary disorder predominates over permeability disorder as in recent phase-field models of spontaneous imbibition. Our results reveal a remarkable connection between imbibition and adsorption as also suggested by recent experiments. The imbibition front is always preceded by a precursor film and the classical Lucas-Washburn scaling law is generally recovered, although some deviations may exist at large porosity. Moreover, the interface roughening is modified by wetting and confinement effects. Our results suggest that the interpretation of the recent experiments should be revised.Comment: 13 pages, 16 figure

The T=0 RFIM on a Bethe lattice: correlation functions along the hysteresis loop

We consider the Gaussian random field Ising model (RFIM) on the Bethe lattice at zero temperature in the presence of a uniform external field and derive the exact expressions of the two-point spin-spin and spin-random field correlation functions along the saturation hysteresis loop. To complete the analytical description and suggest possible approximations for the RFIM on Euclidian lattices we also compute the corresponding direct correlation functions (or proper vertices) and show that they decay rapidly with the distance in the weak-coupling/large disorder regime; their range, however, is not limited to the nearest-neighbor distance.Comment: 13 pages, 7 figure