Generally covariant state-dependent diffusion

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously defined. They typically do not relax to equilibrium steady states even in the absence of extenal forces. Assuming both coordinate covariance and gauge invariance, we derive a second-order Langevin equation with state-dependent diffusion matrix and vanishing environmental forces. It differs from previous proposals but nevertheless entails the Einstein relation, a Maxwellian conditional steady state for the velocities, and the equipartition theorem. The over-damping limit leads to a stochastic differential equation in state space that cannot be interpreted as a pure differential (Ito, Stratonovich or else). At odds with the latter interpretations, the corresponding Fokker-Planck equation admits an equilibrium steady state; a detailed comparison with other theories of state-dependent diffusion is carried out. We propose this as a theory of diffusion in a heat bath with varying temperature. Besides equilibrium, a crucial experimental signature is the non-uniform steady spatial distribution.Comment: 24 page

Nonequilibrium thermodynamics as a gauge theory

We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.Comment: 6 pages. Non-fatal errors in eq.(6), eq.(26) and eq.(31) have been amende

Brownian Carnot engine

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Despite its potential relevance for the development of a thermodynamics of small systems, an experimental study of microscopic Carnot engines is still lacking. Here we report on an experimental realization of a Carnot engine with a single optically trapped Brownian particle as working substance. We present an exhaustive study of the energetics of the engine and analyze the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency -an insight that could inspire novel strategies in the design of efficient nano-motors.Comment: 7 pages, 7 figure

Laboratory study on the mobility of major species in fly ash–brine co-disposal systems: up-flow percolation test

Apart from the generation of fly ash, brine (hyper-saline wastewater) is also a waste material generated in South African power stations as a result of water re-use. These waste materials contain major species such as Al, Si, Na, K, Ca, Mg, Cl and SO4. The co-disposal of fly ash and brine has been practiced by some power stations in South Africa with the aim of utilizing the fly ash to capture the salts in brine. The effect of the chemical interaction of the species contained in both fly ash and brine, when co-disposed, on the mobility of species in the fly ash–brine systems is the focus of this study. The up-flow percolation test was employed to determine the mobility of some major species in the fly ash–brine systems. The results of the analysed eluates from the up-flow percolation tests revealed that some species such as Al, Ca and Na were leached from the fly ash into the brine solution while some species such as Mg, Cl and SO4 were removed to some extent from the brine solution during the interaction with fly ash. The pH of the up-flow percolation systems was observed to play a significant role on the mobility of major species from the fly ash–brine systems. The study showed that some major species such as Mg, Cl and SO4 could be removed from brine solution using fly ash when certain amount of brine percolates through the ash.Web of Scienc

Broken seniority symmetry in the semimagic proton mid-shell nucleus ⁹⁵Rh

Lifetime measurements of low-lying excited states in the semimagic ( N = 50 ) nucleus 95Rh have been performed by means of the fast-timing technique. The experiment was carried out using γ -ray detector arrays consisting of LaBr3(Ce) scintillators and germanium detectors integrated into the DESPEC experimental setup commissioned for the Facility for Antiproton and Ion Research (FAIR) Phase-0, Darmstadt, Germany. The excited states in 95Rh were populated primarily via the β decays of 95Pd nuclei, produced in the projectile fragmentation of a 850 MeV/nucleon 124Xe beam impinging on a 4 g / cm2 9Be target. The deduced electromagnetic E2 transition strengths for the γ -ray cascade within the multiplet structure depopulating from the isomeric Iπ = 21 / 2+ state are found to exhibit strong deviations from predictions of standard shell model calculations which feature approximately conserved seniority symmetry. In particular, the observation of a strongly suppressed E2 strength for the 13 / 2+ → 9 / 2+ ground state transition cannot be explained by calculations employing standard interactions. This remarkable result may require revision of the nucleon-nucleon interactions employed in state-of-the-art theoretical model calculations, and might also point to the need for including three-body forces in the Hamiltonian

Fast-timing measurements in ⁹⁶Pd:improved accuracy for the lifetime of the 4⁺₁ state

Direct lifetime measurements via γ–γ coincidences using the FATIMA fast-timing LaBr3(Ce) array were performed for the excited states below previously reported isomers. In the N = 50 semi-magic 96Pd nucleus, lifetimes below the I π = 8+ seniority isomer were addressed as a benchmark for further analysis. The results for the I π = 2+ and 4 + states confirm the published values. Increased accuracy for the lifetime value was achieved for the 4 + state.peerReviewe