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Register a new userThe Thermodynamics of Social Processes: The Teen Birth Phenomenon
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We argue that a process of social interest is a balance of order and randomness, thereby producing a departure from a stationary diffusion process. The strength of this effect vanishes if the order to randomness intensity ratio vanishes, and this property allows us to reveal, although in an indirect way, the existence of a finite order to randomness intensity ratio. We aim at detecting this effect. We introduce a method of statistical analysis alternative to the compression procedures, with which the limitations of the traditional Kolmogorov-Sinai approach are bypassed. We prove that this method makes it possible for us to build up a memory detector, which signals the presence of even very weak memory, provided that this is persistent over large time intervals. We apply the analysis to the study of the teen birth phenomenon and we find that the unmarried teen births are a manifestation of a social process with a memory more intense than that of the married teens. We attempt to give a social interpretation of this effect.
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This PhD thesis deals with the Markov picture of developed turbulence from the theoretical point of view. The thesis consists of two parts. The first part introduces stochastic thermodynamics, the second part aims at transferring the concepts of stochastic thermodynamics to developed turbulence. / Central in stochastic thermodynamics are Markov processes. An elementary example is Brownian motion. In contrast to macroscopic thermodynamics, the work done and the entropy produced for single trajectories of the Brownian particles are random quantities. Statistical properties of such fluctuating quantities are central in the field of stochastic thermodynamics. Prominent results are so-called fluctuation theorems which express the balance between production and consumption of entropy and generalise the second law. / Turbulent cascades of eddies are assumed to be the predominant mechanism of turbulence generation and fix the statistical properties of developed turbulent flows. An intriguing phenomenon of developed turbulence, known as small-scale intermittency, are violent small-scale fluctuations in flow velocity that exceed any Gaussian prediction. / In analogy to Brownian motion, it is demonstrated in the thesis how the assumption of the Markov property leads to a Markov process for the turbulent cascade that is equivalent to the seminal K62 model. In addition to the K62 model, it is demonstrated how many other models of turbulence can be written as a Markov process, including scaling laws, multiplicative cascades, multifractal models and field-theoretic approaches. Based on the various Markov processes, the production of entropy along the cascade and the corresponding fluctuation theorems is discussed. In particular, experimental data indicates that entropy consumption is linked to small-scale intermittency, and a connection between entropy consumption and an inverse cascade is suggestive.
Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nano-scale system from one equilibrium state to another in finite time, Schmiedl and Seifert ({it Phys. Rev. Lett.} {bf 98}, 108301 (2007)) found the Euler-Lagrange equation to be a non-local integro-differential equation of correlation functions. For two linear examples, we show how this integro-differential equation can be solved analytically. For non-linear physical systems we show how the optimal protocol can be found numerically and demonstrate that there may exist several distinct optimal protocols simultaneously, and we present optimal protocols that have one, two, and three jumps, respectively.
Systems with absorbing configurations usually lead to a unique stationary probability measure called quasi stationary state (QSS) defined with respect to the survived samples. We show that the birth death diffusion (BBD) processes exhibit universal phases and phase transitions when the birth and death rates depend on the instantaneous particle density and their time scales are exponentially separated from the diffusion rates. In absence of birth, these models exhibit non-unique QSSs and lead to an absorbing phase transition (APT) at some critical nonzero death rate; the usual notion of universality is broken as the critical exponents of APT here depend on the initial density distribution.
Hydrodynamics, a term apparently introduced by Daniel Bernoulli (1700-1783) to comprise hydrostatic and hydraulics, has a long history with several theoretical approaches. Here, after a descriptive introduction, we present so-called mesoscopic hydro-thermodynamics, which is also referred to as higher-order generalized hydrodynamics, built within the framework of a mechanical-statistical formalism. It consists of a description of the material and heat motion of fluids in terms of the corresponding densities and their associated fluxes of all orders. In this way, movements are characterized in terms of intermediate to short wavelengths and intermediate to high frequencies. The fluxes have associated Maxwell-like times, which play an important role in determining the appropriate contraction of the description (of the enormous set of fluxes of all orders) necessary to address the characterization of the motion in each experimental setup. This study is an extension of a preliminary article: Physical Review E textbf{91}, 063011 (2015).
For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects, the optimal protocol has been found to involve jumps of the control parameter at the beginning and end of the process. Including the inertia term, we show that this feature not only persists but that even delta peak-like changes of the control parameter at both boundaries make the process optimal. These results are obtained by analyzing two simple paradigmatic cases: First, a Brownian particle dragged by a harmonic optical trap through a viscous fluid and, second, a Brownian particle subject to an optical trap with time-dependent stiffness. These insights could be used to improve free energy calculations via either thermodynamic integration or fast growth methods using Jarzynskis equality.
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