Superpositions of probability distributions

Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap

We consider passive Brownian particles trapped in an "imperfect" harmonic trap. The trap is imperfect because it is randomly turned off and on, and as a result particles fail to equilibrate. Another way to think about this is to say that a harmonic trap is time dependent on account of its strength evolving stochastically in time. Particles in such a system are passive and activity arises through external control of a trapping potential, thus, no internal energy is used to power particle motion. A stationary Fokker-Planck equation of this system can be represented as a third-order differential equation, and its solution, a stationary distribution, can be represented as a superposition of Gaussian distributions for different strengths of a harmonic trap. This permits us to interpret a stationary system as a system in equilibrium with quenched disorder.

Tsallis thermostatics as a statistical physics of random chains

In this paper we point out that the generalized statistics of Tsallis-Havrda-Charvát can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we use the path-integral approach to show that the ensuing partition function can be identified with the partition function of a fluctuating oriented random loop of arbitrary length and shape in a background scalar potential. To put some meat on the bare bones, we illustrate this with two statistical systems: Schultz-Zimm polymer and relativistic particle. Further salient issues such as the projective special linear group PSL(2,R) transformation properties of Tsallis' inverse-temperature parameter and a grand-canonical ensemble of fluctuating random loops related to the Tsallis-Havrda-Charvát statistics are also briefly discussed.

Fluctuating noise drives Brownian transport

The transport properties of Brownian ratchet were studied in the presence of stochastic intensity noise in both overdamped and underdamped regimes. In the overdamped case, an analytical solution using the matrix-continued fraction method revealed the existence of a maximum current when the noise intensity fluctuates on intermediate timescale regions. Similar effects were observed for the underdamped case by Monte Carlo simulations. The optimal time-correlation for Brownian transport coincided with the experimentally observed time-correlation of the extrinsic noise in Escherichia coli gene expression and implied the importance of environmental noise for molecular mechanisms.

Generalization of the Beck-Cohen superstatistics

Generalized superstatistics, i.e., a "statistics of superstatistics," is proposed. A generalized superstatistical system comprises a set of superstatistical subsystems and represents a generalized hyperensemble. There exists a random control parameter that determines both the density of energy states and the distribution of the intensive parameter for each superstatistical subsystem, thereby forming the third, upper level of dynamics. Generalized superstatistics can be used for nonstationary nonequilibrium systems. The system in which a supercritical multitype age-dependent branching process takes place is an example of a nonstationary generalized superstatistical system. The theory is applied to pair production in a neutron star magnetosphere.

Generalized statistical mechanics for superstatistical systems

Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex system onto a system of ordinary statistical mechanics with modified energy levels. We also briefly review recent examples of applications of the superstatistics concept for three very different subject areas, namely train delay statistics, turbulent tracer dynamics and cancer survival statistics.

Superstatistical distributions from a maximum entropy principle

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: the superstatistical quantum-mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.