Open Markov processes: A compositional perspective on non-equilibrium steady states in biology

In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These `open Markov processes' serve as the building blocks for more complicated processes. In this paper, we describe the potential application of this framework in the modeling of biological systems as open systems maintained away from equilibrium. We show that non-equilibrium steady states emerge in open systems of this type, even when the rates of the underlying process are such that a detailed balanced equilibrium is permitted. It is shown that these non-equilibrium steady states minimize a quadratic form which we call `dissipation.' In some circumstances, the dissipation is approximately equal to the rate of change of relative entropy plus a correction term. On the other hand, Prigogine's principle of minimum entropy production generally fails for non-equilibrium steady states. We use a simple model of membrane transport to illustrate these concepts

A Second Law for Open Markov Processes

In this paper we define the notion of an open Markov process. An open Markov process is a generalization of an ordinary Markov process in which populations are allowed to flow in and out of the system at certain boundary states. We show that the rate of change of relative entropy in an open Markov process is less than or equal to the flow of relative entropy through its boundary states. This can be viewed as a generalization of the Second Law for open Markov processes. In the case of a Markov process whose equilibrium obeys detailed balance, this inequality puts an upper bound on the rate of change of the free energy for any non-equilibrium distribution.Comment: 9 pages, 3 figure

Dimethyl disulfide (DMDS) and dimethyl sulfide (DMS) emissions from biomass burning in Australia

We identify dimethyl disulfide (DMDS) as the major reduced sulfur-containing gas emitted from bushfires in Australia's Northern Territory. Like dimethyl sulfide (DMS), DMDS is oxidized in the atmosphere to sulfur dioxide (SO2) and methane sulfonic acid (MSA), which are intermediates in the formation of sulfuric acid (H2SO4). The mixing ratios of DMDS and DMS were the highest we have ever detected, with maximum values of 113 and 35 ppbv, respectively, whereas background values were below the detection limit (10 pptv). Molar emission ratios relative to carbon monoxide (CO) were [1.6 ± 0.1] × 10-5 and [6.2 ± 0.3] × 10-6, for DMDS and DMS respectively, while molar emission ratios relative to carbon dioxide (CO2) were [4.7 ± 0.4] × 10 6 and [1.4 ± 0.4] × 10 7, respectively. Assuming these observations are representative of biomass burning, we estimate that biomass burning could yield up to 175 Gg/yr of DMDS (119 Gg S/yr) and 13 Gg/yr of DMS

A measurement of the radiation dose to LDEF by passive dosimetry

The results from a pair of thermoluminescent dosimeter experiments flown aboard the Long Duration Exposure Facility (LDEF) show an integrated dose several times smaller than that predicted by the NASA environmental models for shielding thicknesses much greater than 0.10 gm/sq cm aluminum. For thicknesses between 0.01 and 0.1 gm/sq cm, the measured dose was in agreement with predictions. The Space and Environment Technology Center of The Aerospace Corporation fielded two related experiments on LDEF to measure the energetic radiation dose by means of passive dosimetry. The sensors were LiF thermoluminescent dosimeters mounted behind various thicknesses of shielding. The details of the experiment are described first, followed by the results of the observations. A comparison is made with the predictions based upon the NASA environmental models and the actual mission profile flown by LDEF; conclusions follow

Relative Entropy in Biological Systems

In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy - that is, the Kullback--Leibler divergence, or various generalizations of this - provides a quantitative measure of how far from equilibrium the system is. We explain various theorems that give conditions under which relative entropy is nonincreasing. In biochemical applications these results can be seen as versions of the Second Law of Thermodynamics, stating that free energy can never increase with the passage of time. In ecological applications, they make precise the notion that a population gains information from its environment as it approaches equilibrium.Comment: 20 page

SO₂ emissions from basaltic eruptions, and the excess sulfur issue

Volcanic SO2 can affect the Earth's environment. Where no direct measurements of SO2 in the atmosphere are available, a petrologic method of assessing sulfur release from the magma must be used. However, in studies of arc-derived eruptions, satellite-based measurements of SO2 emissions using Total Ozone Mapping Spectrometer (TOMS) data are orders of magnitude greater than those calculated petrologically, implying that a separate S-rich gas phase in the magma chamber may be responsible for the excess sulfur. We test whether this applies in other settings. For Icelandic and Hawaiian basalts we find that petrologic SO2 values are comparable to measurements of SO2 by TOMS. Thus, for non-arc basalts, the petrologic method gives reliable estimates of SO2 released. The implied absence of excess sulfur in non-arc basaltic magmas is a reflection of source magma conditions, notably lower fO2 and volatile contents than arc magmas, inhibiting the exsolution of a S-rich gas prior to eruption

Isolation and characterisation of 2-Tert-butyl-8-hydroxyquinoline as a crystalline solid and its blue fluorescent Li complex

Copyright © 2014 Poopathy Kathirgamanathan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.2-Tert-butyl-8-hydroxyquinoline (2-TB-8-hq) has been isolated as a crystalline solid and its X-ray structure elucidated, resolving three decades of controversy, since it was previously wrongly reported as yellow oil by some other workers. An improved synthetic method has been developed which increases the yield from 20% to 60%. The lithium complex of 2-TB-8-hq is blue emitting and the HOMO and LUMO levels are lowered by 0.86 eV and 0.74 eV, respectively, compared with the parent lithium 8-hydroxyquinolinolate (Li 8-hq)

Herschel/HIFI detections of hydrides towards AFGL 2591: Envelope emission versus tenuous cloud absorption

The Heterodyne Instrument for the Far Infrared (HIFI) onboard the Herschel Space Observatory allows the first observations of light diatomic molecules at high spectral resolution and in multiple transitions. Here, we report deep integrations using HIFI in different lines of hydrides towards the high-mass star forming region AFGL 2591. Detected are CH, CH^+, NH, OH^+, H_2O^+, while NH^+ and SH^+ have not been detected. All molecules except for CH and CH^+ are seen in absorption with low excitation temperatures and at velocities different from the systemic velocity of the protostellar envelope. Surprisingly, the CH(J_(F,P) = 3/2_(2,−) − 1/2_(1,+)) and CH^+(J = 1−0, J = 2−1) lines are detected in emission at the systemic velocity. We can assign the absorption features to a foreground cloud and an outflow lobe, while the CH and CH^+ emission stems from the envelope. The observed abundance and excitation of CH and CH^+ can be explained in the scenario of FUV irradiated outflow walls, where a cavity etched out by the outflow allows protostellar FUV photons to irradiate and heat the envelope at larger distances driving the chemical reactions that produce these molecules