Winning combinations of history-dependent games

The Parrondo effect describes the seemingly paradoxical situation in which two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24 (2000)]. Here we generalize this analysis to the case where both games are history-dependent, i.e. there is an intrinsic memory in the dynamics of each game. New results are presented for the cases of both random and periodic switching between the two games.Comment: (6 pages, 7 figures) Version 2: Major cosmetic changes and some minor correction

Inattainability of Carnot efficiency in the Brownian heat engine

We discuss the reversibility of Brownian heat engine. We perform asymptotic analysis of Kramers equation on B\"uttiker-Landauer system and show quantitatively that Carnot efficiency is inattainable even in a fully overdamping limit. The inattainability is attributed to the inevitable irreversible heat flow over the temperature boundary.Comment: 5 pages, to appear in Phys. Rev.

Comprehensive study of phase transitions in relaxational systems with field-dependent coefficients

We present a comprehensive study of phase transitions in single-field systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift combined with collective effects, but is instead similar to the one associated with noise-induced transitions a la Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Ito vs Stratonvich) merely shifts the phase boundaries. With the help of a mean-field approximation, we present a broad qualitative picture of the various phase diagrams that can be found in these systems. To complement the theoretical analysis we present numerical simulations that confirm the findings of the mean-field theory

Spatial Patterns Induced Purely by Dichotomous Disorder

We study conditions under which spatially extended systems with coupling a la Swift-Hohenberg exhibit spatial patterns induced purely by the presence of quenched dichotomous disorder. Complementing the theoretical results based on a generalized mean-field approximation, we also present numerical simulations of particular dynamical systems that exhibit the proposed phenomenology

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations

Energetics of rocked inhomogeneous ratchets

We study the efficiency of frictional thermal ratchets driven by finite frequency driving force and in contact with a heat bath. The efficiency exhibits varied behavior with driving frequency. Both nonmonotonic and monotonic behavior have been observed. In particular the magnitude of efficiency in finite frequency regime may be more than the efficiency in the adiabatic regime. This is our central result for rocked ratchets. We also show that for the simple potential we have chosen, the presence of only spatial asymmetry (homogeneous system) or only frictional ratchet (symmetric potential profile), the adiabatic efficiency is always more than in the nonadiabatic case.Comment: 5 figure

Exact formula for currents in strongly pumped diffusive systems

We analyze a generic model of mesoscopic machines driven by the nonadiabatic variation of external parameters. We derive a formula for the probability current; as a consequence we obtain a no-pumping theorem for cyclic processes satisfying detailed balance and demonstrate that the rectification of current requires broken spatial symmetry.Comment: 10 pages, accepted for publication in the Journal of Statistical Physic

Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States

We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or antiferromagnetic ordered states. We discuss the phase diagram, the order of the transitions, and the critical behaviour. For global coupling we show analytically that the critical exponent of the magnetization exhibits a transition from the value 1/2 to a non-universal behaviour depending on the ratio of noise strength to the magnitude of the spatial coupling.Comment: 4 pages, 5 figure

Noise-Induced Phase Separation: Mean-Field Results

We present a study of a phase-separation process induced by the presence of spatially-correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of the model. Mean-field results are compared with numerical simulations of the complete model in two dimensions. Additionally, a comparison between the noise-driven dynamics of conserved and nonconserved systems is made at the level of the mean-field approximation.Comment: 12 pages (including 6 figures) LaTeX file. Submitted to Phys. Rev.