Lasting effects of static magnetic field on classical Brownian motion.

The Bohr-Van Leeuwen theorem states that an external static magnetic field does not influence the state of a classical equilibrium system: There is no equilibrium classical magnetism, since the magnetic field does not do work. We revisit this famous no-go result and consider a classical charged Brownian particle interacting with an equilibrium bath. We confirm that the Bohr-Van Leeuwen theorem holds for the long-time (equilibrium) state of the particle. But the external static, homogeneous magnetic field does influence the long-time state of the thermal bath, which is described via the Caldeira-Leggett model. In particular, the magnetic field induces an average angular momentum for the (uncharged) bath, which separates into two sets rotating in opposite directions. The effect relates to the bath going slightly out of equilibrium under the influence of the Brownian particle and persists for arbitrarily long times. In this context we studied the behavior of the two other additive integrals of motion, energy, and linear momentum. The situation with linear momentum is different, because it is dissipated away by (and from) the bath modes. The average energy of the bath mode retains the magnetic field as a small correction. Thus, only the bath angular momentum really feels the magnetic field for long times.

Energy Cost of Dynamical Stabilization: Stored versus Dissipated Energy.

Dynamical stabilization processes (homeostasis) are ubiquitous in nature, but the needed energetic resources for their existence have not been studied systematically. Here, we undertake such a study using the famous model of Kapitza's pendulum, which has attracted attention in the context of classical and quantum control. This model is generalized and rendered autonomous, and we show that friction and stored energy stabilize the upper (normally unstable) state of the pendulum. The upper state can be rendered asymptotically stable, yet it does not cost any constant dissipation of energy, and only a transient energy dissipation is needed. Asymptotic stability under a single perturbation does not imply stability with respect to multiple perturbations. For a range of pendulum-controller interactions, there is also a regime where constant energy dissipation is needed for stabilization. Several mechanisms are studied for the decay of dynamically stabilized states.

Nonequilibrium, weak-field-induced cyclotron motion: A mechanism for magnetobiology.

There is a long-time quest for understanding physical mechanisms of weak magnetic field interaction with biological matter. Two factors impeded the development of such mechanisms: first, a high (room) temperature of a cellular environment, where a weak, static magnetic field induces a (classically) zero equilibrium response. Second, the friction in the cellular environment is large, preventing a weak field to alter nonequilibrium processes such as a free diffusion of charges. Here we study a class of nonequilibrium steady states of a cellular ion in a confining potential, where the response to a (weak, homogeneous, static) magnetic field survives strong friction and thermal fluctuations. The magnetic field induces a rotational motion of the ion that proceeds with the cyclotron frequency. Such nonequilibrium states are generated by a white noise acting on the ion additionally to the nonlocal (memory-containing) friction and noise generated by an equilibrium thermal bath. The intensity of this white noise can be weak, i.e., much smaller than the thermal noise intensity.

Polymorphism in rapidly changing cyclic environment.

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric payoffs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic (fine-grained) environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a nonlinear fitness that is induced by environmental changes. The nonlinear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is exemplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.

Emergence of Leadership in Communication.

We study a neuro-inspired model that mimics a discussion (or information dissemination) process in a network of agents. During their interaction, agents redistribute activity and network weights, resulting in emergence of leader(s). The model is able to reproduce the basic scenarios of leadership known in nature and society: laissez-faire (irregular activity, weak leadership, sizable inter-follower interaction, autonomous sub-leaders); participative or democratic (strong leadership, but with feedback from followers); and autocratic (no feedback, one-way influence). Several pertinent aspects of these scenarios are found as well-e.g., hidden leadership (a hidden clique of agents driving the official autocratic leader), and successive leadership (two leaders influence followers by turns). We study how these scenarios emerge from inter-agent dynamics and how they depend on behavior rules of agents-in particular, on their inertia against state changes.

Stochastic Model for Phonemes Uncovers an Author-Dependency of Their Usage.

We study rank-frequency relations for phonemes, the minimal units that still relate to linguistic meaning. We show that these relations can be described by the Dirichlet distribution, a direct analogue of the ideal-gas model in statistical mechanics. This description allows us to demonstrate that the rank-frequency relations for phonemes of a text do depend on its author. The author-dependency effect is not caused by the author's vocabulary (common words used in different texts), and is confirmed by several alternative means. This suggests that it can be directly related to phonemes. These features contrast to rank-frequency relations for words, which are both author and text independent and are governed by the Zipf's law.

Opinion dynamics with confirmation bias.

BACKGROUND: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical research of this phenomenon has mainly focused on its economic implications possibly missing its potential connections with broader notions of cognitive science. METHODOLOGY/PRINCIPAL FINDINGS: We formulate a (non-Bayesian) model for revising subjective probabilistic opinion of a confirmationally-biased agent in the light of a persuasive opinion. The revision rule ensures that the agent does not react to persuasion that is either far from his current opinion or coincides with it. We demonstrate that the model accounts for the basic phenomenology of the social judgment theory, and allows to study various phenomena such as cognitive dissonance and boomerang effect. The model also displays the order of presentation effect-when consecutively exposed to two opinions, the preference is given to the last opinion (recency) or the first opinion (primacy) -and relates recency to confirmation bias. Finally, we study the model in the case of repeated persuasion and analyze its convergence properties. CONCLUSIONS: The standard Bayesian approach to probabilistic opinion revision is inadequate for describing the observed phenomenology of persuasion process. The simple non-Bayesian model proposed here does agree with this phenomenology and is capable of reproducing a spectrum of effects observed in psychology: primacy-recency phenomenon, boomerang effect and cognitive dissonance. We point out several limitations of the model that should motivate its future development.

Stabilization and anomalous hydration of collagen fibril under heating.

BACKGROUND: Type I collagen is the most common protein among higher vertebrates. It forms the basis of fibrous connective tissues (tendon, chord, skin, bones) and ensures mechanical stability and strength of these tissues. It is known, however, that separate triple-helical collagen macromolecules are unstable at physiological temperatures. We want to understand the mechanism of collagen stability at the intermolecular level. To this end, we study the collagen fibril, an intermediate level in the collagen hierarchy between triple-helical macromolecule and tendon. METHODOLOGY/PRINCIPAL FINDING: When heating a native fibril sample, its Young's modulus decreases in temperature range 20-58°C due to partial denaturation of triple-helices, but it is approximately constant at 58-75°C, because of stabilization by inter-molecular interactions. The stabilization temperature range 58-75°C has two further important features: here the fibril absorbs water under heating and the internal friction displays a peak. We relate these experimental findings to restructuring of collagen triple-helices in fibril. A theoretical description of the experimental results is provided via a generalization of the standard Zimm-Bragg model for the helix-coil transition. It takes into account intermolecular interactions of collagen triple-helices in fibril and describes water adsorption via the Langmuir mechanism. CONCLUSION/SIGNIFICANCE: We uncovered an inter-molecular mechanism that stabilizes the fibril made of unstable collagen macromolecules. This mechanism can be relevant for explaining stability of collagen.

Carnot cycle at finite power: attainability of maximal efficiency.

We want to understand whether and to what extent the maximal (Carnot) efficiency for heat engines can be reached at a finite power. To this end we generalize the Carnot cycle so that it is not restricted to slow processes. We show that for realistic (i.e., not purposefully designed) engine-bath interactions, the work-optimal engine performing the generalized cycle close to the maximal efficiency has a long cycle time and hence vanishing power. This aspect is shown to relate to the theory of computational complexity. A physical manifestation of the same effect is Levinthal's paradox in the protein folding problem. The resolution of this paradox for realistic proteins allows to construct engines that can extract at a finite power 40% of the maximally possible work reaching 90% of the maximal efficiency. For purposefully designed engine-bath interactions, the Carnot efficiency is achievable at a large power.

Explaining Zipf's law via a mental lexicon.

Zipf's law is the major regularity of statistical linguistics that has served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that Zipf's law-together with its applicability for a single text and its generalizations to high and low frequencies including hapax legomena-can be derived from assuming that the words are drawn into the text with random probabilities. Their a priori density relates, via the Bayesian statistics, to the mental lexicon of the author who produced the text.

Comment on "Cooling by heating: refrigeration powered by photons".

A Comment on the Letter by B. Cleuren, B. Rutten, and C. Van den Broeck, Phys. Rev. Lett. 108, 120603 (2012). The authors of the Letter offer a Reply.

Thermodynamic limits of dynamic cooling.

We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature T(min)>0 reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir and over the reservoir energy spectrum. The minimal work needed to reach T(min) grows as 1/T(min). This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above T(min). Our results on T(min)>0 prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. We also study cooling via a reservoir consisting of N≫1 identical spins. Here we show that T(min)∝1/N and find the maximal cooling compatible with the minimal work determined by the free energy. Finally we discuss cooling by reservoir with an initially microcanonic state and show that although a purely microcanonic state can yield the zero temperature, the unattainability is recovered when taking into account imperfections in preparing the microcanonic state.

Le Chatelier's principle in replicator dynamics.

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both types of equilibria satisfy the detailed balance condition.

Optimal refrigerator.

We study a refrigerator model which consists of two n -level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures T h and T c, respectively (θ ≡ T c/T h < 1). The refrigerator functions in two steps: thermally isolated interaction between the systems driven by the external field and isothermal relaxation back to equilibrium. There is a complementarity between the power of heat transfer from the cold bath and the efficiency: the latter nullifies when the former is maximized and vice versa. A reasonable compromise is achieved by optimizing the product of the heat-power and efficiency over the Hamiltonian of the two systems. The efficiency is then found to be bounded from below by [formula: see text] (an analog of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency [formula: see text]. The lower bound is reached in the equilibrium limit θ → 1. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for ln n >> 1. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by ζ CA and converges to it for n >> 1.

Replicators in a fine-grained environment: adaptation and polymorphism.

Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multiplayer replicator dynamics in a constant environment. The two-player terms correspond to the time-averaged payoffs, while the three- and four-player terms arise from the adaptation of the morphs to their varying environment. Such multiplayer terms can induce a stable polymorphism. The establishment of the polymorphism in partnership games [genetic selection] is accompanied by decreasing mean fitness of the population.

Work extremum principle: structure and function of quantum heat engines.

We consider a class of quantum heat engines consisting of two subsystems interacting with a work-source and coupled to two separate baths at different temperatures Th>Tc. The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addition, its efficiency is bounded from below by the Curzon-Ahlborn value 1-radical Tc/Th and from above by the Carnot value 1-(Tc/Th). The latter is reached-at finite power--for a macroscopic engine, while the former is achieved in the equilibrium limit Th-->Tc . The efficiency that maximizes the power is strictly larger than the Curzon-Ahloborn value. When the work is maximized at a zero power, even a small (few-level) engine extracts work right at the Carnot efficiency.