What is the probability of a thermodynamical transition?

If the second law of thermodynamics forbids a transition from one state to another, then it is still possible to make the transition happen by using a sufficient amount of work. But if we do not have access to this amount of work, can the transition happen probabilistically? In the thermodynamic limit, this probability tends to zero, but here we find that for finite-sized systems, it can be finite. We compute the maximum probability of a transition or a thermodynamical fluctuation from any initial state to any final state, and show that this maximum can be achieved for any final state which is block-diagonal in the energy eigenbasis. We also find upper and lower bounds on this transition probability, in terms of the work of transition. As a bi-product, we introduce a finite set of thermodynamical monotones related to the thermo-majorization criteria which governs state transitions, and compute the work of transition in terms of them. The trade-off between the probability of a transition, and any partial work added to aid in that transition is also considered. Our results have applications in entanglement theory, and we find the amount of entanglement required (or gained) when transforming one pure entangled state into any other.Comment: 15+6 pages, 7+1 figures V3: Added discussion on heralded probability and relation to fluctuation theorems. V2: Emphasized that X can be any state and that the achievability of our result in the full thermodynamics case, holds only when the target state is block-diagonal in the energy eigenbasi

Entanglement fluctuation theorems

Pure state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many copy level, but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, which is formally identical to the Jarzynski fluctuation equality found in thermodynamics. One can also relate a forward entanglement transformation to its reverse process in terms of the entanglement cost of such a transformation, in a manner equivalent to the Crooks relation. We show that a strong converse theorem for entanglement transformations is formally related to the second law of thermodynamics, while the fact that the Schmidt rank of an entangled state cannot increase is related to the third law of thermodynamics. Achievability of the protocols is done by introducing an entanglement battery, a device which stores entanglement and uses an amount of entanglement that is allowed to fluctuate but with an average cost which is still optimal. This allows us to also solve the problem of partial entanglement recovery, and in fact, we show that entanglement is fully recovered. Allowing the amount of consumed entanglement to fluctuate also leads to improved and optimal entanglement dilution protocols.Comment: comments welcome, v2 published versio

The second law of quantum thermodynamics as an equality

We investigate the connection between recent results in quantum thermodynamics and fluctuation relations by adopting a fully quantum mechanical description of thermodynamics. By including a work system whose energy is allowed to fluctuate, we derive a set of equalities which all thermodynamical transitions have to satisfy. This extends the condition for maps to be Gibbs-preserving to the case of fluctuating work, providing a more general characterisation of maps commonly used in the information theoretic approach to thermodynamics. For final states, block diagonal in the energy basis, this set of equalities are necessary and sufficient conditions for a thermodynamical state transition to be possible. The conditions serves as a parent equation which can be used to derive a number of results. These include writing the second law of thermodynamics as an equality featuring a fine-grained notion of the free energy. It also yields a generalisation of the Jarzynski fluctuation theorem which holds for arbitrary initial states, and under the most general manipulations allowed by the laws of quantum mechanics. Furthermore, we show that each of these relations can be seen as the quasi-classical limit of three fully quantum identities. This allows us to consider the free energy as an operator, and allows one to obtain more general and fully quantum fluctuation relations from the information theoretic approach to quantum thermodynamics.Comment: 11+3 pages. V4: Updated to match published version. Discussion of thermo-majorization and implementing arbitary unitaries added. V3: Added funding information. V2: Expanded discussion on relation to fluctuation theorem

HABITAT UTILIZATION BY THE TEXAS HORNED LIZARD (PHRYNOSOMA CORNUTUM) FROM TWO SITES IN CENTRAL TEXAS

The Texas Horned Lizard (Phrynosoma cornutum) is found in a variety of habitats. Although several studies have been conducted on habitat use by this species, none have been performed in central Texas, a more mesic habitat than most of those previously studied. This area is of special interest because horned lizard populations have been experiencing sharp declines in central Texas over the last approximately 50 years. We collected habitat data at two sites in central Texas, Camp Bowie and Blue Mountain Peak Ranch. Microhabitat data included canopy cover and ground cover from digitized photographs of Daubenmire quadrats; macrohabitat variables included vegetation height and length, cactus height, soil penetrability, woody plant species richness, tree density, tree diameter at breast height (DBH), and density of ant mounds collected along 100-m by 2-m transects. Similar patterns of habitat use were observed between the two sites. At Blue Mountain Peak Ranch, lizards appeared to be located in areas with a diversity of ground cover types, as observed in previous studies. At Camp Bowie, vegetation encroachment limited lizards in some areas to the use of roads and road margins. Implementation of prescribed burns or other vegetation management could create the preferred ground cover mosaic at such sites

An EPR investigation of binding environments by N-donor chelating exchange resins for Cu extraction from aqueous media

EPR and UV−vis spectroscopy were collectively used to characterize a series of Cu(II) binding environments within two chelating exchange resins, Dowex and CuWRAM, used for Cu(II) extraction from aqueous media. A series of well-defined intra- and intermolecular binding sites have been identified as responsible for Cu(II) uptake

Predicting preferential DNA vector insertion sites: implications for functional genomics and gene therapy

Viral and transposon vectors have been employed in gene therapy as well as functional genomics studies. However, the goals of gene therapy and functional genomics are entirely different; gene therapists hope to avoid altering endogenous gene expression (especially the activation of oncogenes), whereas geneticists do want to alter expression of chromosomal genes. The odds of either outcome depend on a vector's preference to integrate into genes or control regions, and these preferences vary between vectors. Here we discuss the relative strengths of DNA vectors over viral vectors, and review methods to overcome barriers to delivery inherent to DNA vectors. We also review the tendencies of several classes of retroviral and transposon vectors to target DNA sequences, genes, and genetic elements with respect to the balance between insertion preferences and oncogenic selection. Theoretically, knowing the variables that affect integration for various vectors will allow researchers to choose the vector with the most utility for their specific purposes. The three principle benefits from elucidating factors that affect preferences in integration are as follows: in gene therapy, it allows assessment of the overall risks for activating an oncogene or inactivating a tumor suppressor gene that could lead to severe adverse effects years after treatment; in genomic studies, it allows one to discern random from selected integration events; and in gene therapy as well as functional genomics, it facilitates design of vectors that are better targeted to specific sequences, which would be a significant advance in the art of transgenesis

Spatial Patterns of Snow Cover in North Carolina: Surface and Satellite Perspectives

Snow mapping is a common practice in regions that receive large amounts of snowfall annually, have seasonally-continuous snow cover, and where snowmelt contributes significantly to the hydrologic cycle. Although higher elevations in the southern Appalachian Mountains average upwards of 100 inches of snow annually, much of the remainder of the Southeast U.S. receives comparatively little snowfall (< 10 inches). Recent snowy winters in the region have provided an opportunity to assess the fine-grained spatial distribution of snow cover and the physical processes that act to limit or improve its detection across the Southeast. In the present work, both in situ and remote sensing data are utilized to assess the spatial distribution of snow cover for a sample of recent snowfall events in North Carolina. Specifically, this work seeks to determine how well ground measurements characterize the fine-grained patterns of snow cover in relation to Moderate- Resolution Imaging Spectroradiometer (MODIS) snow cover products (in this case, the MODIS Fractional Snow Cover product)