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.

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.

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.

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.

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).

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.

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.

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.

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.

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

A Comment on the Letter by B. Cleuren, B. Rutten, and C.

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.

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.

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.

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.

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.