New observations regarding deterministic, time reversible thermostats and Gauss's principle of least constraint

Deterministic thermostats are frequently employed in non-equilibrium molecular dynamics simulations in order to remove the heat produced irreversibly over the course of such simulations. The simplest thermostat is the Gaussian thermostat, which satisfies Gauss's principle of least constraint and fixes the peculiar kinetic energy. There are of course infinitely many ways to thermostat systems, e.g. by fixing $\sum\limits_i{|{p_i}|^{\mu + 1}}$. In the present paper we provide, for the first time, convincing arguments as to why the conventional Gaussian isokinetic thermostat ($\mu=1$) is unique in this class. We show that this thermostat minimizes the phase space compression and is the only thermostat for which the conjugate pairing rule (CPR) holds. Moreover it is shown that for finite sized systems in the absence of an applied dissipative field, all other thermostats ($\mu=1$) perform work on the system in the same manner as a dissipative field while simultaneously removing the dissipative heat so generated. All other thermostats ($\mu=1$) are thus auto-dissipative. Among all $\mu$-thermostats, only the $\mu=1$ Gaussian thermostat permits an equilibrium state.Comment: 27 pages including 10 figures; submitted for publication Journal of Chemical Physic

Note on the Kaplan-Yorke dimension and linear transport coefficients

A number of relations between the Kaplan-Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the transport coefficients in terms of the Kaplan-Yorke dimension is derived. Alternatively, the Kaplan-Yorke dimension for a dissipative macroscopic system can be expressed in terms of the transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.Comment: 12 pages, 5 figures, submitted to J. Stat. Phy

The steady state fluctuation relation for the dissipation function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work

Plant response to solar ultraviolet-B radiation in a southern South American Sphagnum peatland

1. Plant growth and pigmentation of the moss Sphagnum magellanicum and the vascular plants Empetrum rubrum, Nothofagus antarctica and Tetroncium magellanicum were measured under near-ambient (90% of ambient) and reduced (20%) ultraviolet-B (UV-B) radiation for three growing seasons in a Sphagnum peatland in Tierra del Fuego, Argentina (55°S). 2. Reduction of solar UV-B increased height growth but decreased volumetric density in S. magellanicum so that biomass production was not influenced during the 3 years. The morphology of vascular plants tended not to respond to UV-B reduction. 3. A 10-20% decrease in UV-B-absorbing compounds occurred in T. magellanicum under solar UV-B reduction. No effects were seen on chlorophyll or carotenoids in S. magellanicum, although, for UV-B-absorbing compounds, a significant interaction between UV-B and year suggests some response to solar UV-B reduction. 4. The climate-related growth of the dwarf shrub E. rubrum was assessed retrospectively by correlating an 8-year record of annual stem elongation with macroclimatic factors including solar UV-B and visible radiation, precipitation and temperature. 5. No significant negative correlations were found between annual E. rubrum stem elongation and ambient solar UV-B, the ratio of UV-B: visible radiation, or the 305-nm: 340-nm irradiance ratio for an 8-year record (1990-91 to 1997-98), nor was stem elongation affected by solar UV-B reduction in our experimental field plots after 3 years. 6. The role of solar UV-B radiation on plant growth in Sphagnum peatlands in Tierra del Fuego, Argentina, is likely to depend on the severity of stratospheric ozone depletion over the next several decades. The increases in ambient solar UV-B associated with ozone depletion over the last 20 years are less than the difference between our radiation treatments. Therefore, providing that the ozone layer substantially recovers by the middle of this century, only modest effects of increased solar UV-B on plant growth may be expected.Fil: Searles, Peter Stoughton. State University of Utah; Estados UnidosFil: Flint, Stephan D.. State University of Utah; Estados UnidosFil: Diaz, Susana Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Austral de Investigaciones Científicas; ArgentinaFil: Rousseaux, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Ballare, Carlos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Caldwell, Martyn M.. State University of Utah; Estados Unido

Contribution of the stochastic forces to the fluctuation theorem

In some recent papers, the use of random forces has been related to a systematic breakdown of the fluctuation theorem. In the framework of nonequilibrium molecular dynamics, we provide a derivation of this theorem for systems driven by both deterministic and stochastic forces. It turns out that it is still valid and describes the total dissipation, explicitly the sum of two dimensionless works for which fluctuation relations may fail. We numerically study their range of validity, comment on experimental results, and point out in which limit a noise can be neglected

Wall mediated transport in confined spaces: Exact theory for low density

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.Comment: 30 pages, 1 figur

MicroRNA Detection Using a Double Molecular Beacon Approach: Distinguishing Between miRNA and Pre-miRNA

MicroRNAs (miRNAs) are small, noncoding RNAs that post-transcriptionally regulate gene expression and are recognized for their roles both as modulators of disease progression and as biomarkers of disease activity, including neurological diseases, cancer, and cardiovascular disease (CVD). Commonly, miRNA abundance is assessed using quantitative real-time PCR (qRT-PCR), however, qRT-PCR for miRNA can be labor intensive, time consuming, and may lack specificity for detection of mature versus precursor forms of miRNA. Here, we describe a novel double molecular beacon approach to miRNA assessment that can distinguish and quantify mature versus precursor forms of miRNA in a single assay, an essential feature for use of miRNAs as biomarkers for disease. Using this approach, we found that molecular beacons with DNA or combined locked nucleic acid (LNA)-DNA backbones can detect mature and precursor miRNAs (pre-miRNAs) of low (< 1 nM) abundance in vitro. The double molecular beacon assay was accurate in assessing miRNA abundance in a sample containing a mixed population of mature and precursor miRNAs. In contrast, qRT-PCR and the single molecular beacon assay overestimated miRNA abundance. Additionally, the double molecular beacon assay was less labor intensive than traditional qRT-PCR and had 10-25% increased specificity. Our data suggest that the double molecular beacon-based approach is more precise and specific than previous methods, and has the promise of being the standard for assessing miRNA levels in biological samples

Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales

We experimentally demonstrate the fluctuation theorem, which predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales, by following the trajectory of a colloidal particle captured in an optical trap that is translated relative to surrounding water molecules. From each particle trajectory, we calculate the entropy production/consumption over the duration of the trajectory and determine the fraction of second law–defying trajectories. Our results show entropy consumption can occur over colloidal length and time scales