Fluctuation relations for a few observable currents at their own beat

Coarse-grained models are widely used to explain the effective behavior of partially observable physical systems with hidden degrees of freedom. Reduction procedures in state space typically disrupt Markovianity and a fluctuation relation cannot be formulated. A recently developed framework of transition-based coarse-graining gave rise to a fluctuation relation for a single current, while all others are hidden. Here, we extend the treatment to an arbitrary number of observable currents. Crucial for the derivation are the concepts of mixed currents and their conjugated effective affinities, that can be inferred from the time series of observable transitions. We also discuss the connection to generating functions, transient behavior, and how our result recovers the fluctuation relation for a complete set of currents.Comment: 36 pages, 11 figure

Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation $a + b = s^Y$ between the number of fundamental affinities $a$, that of broken conservation laws $b$ and the number of chemostats $s^Y$. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction and of thermodynamic constraints for network reconstruction.Comment: 18 page

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

The shape of the <i>T</i>_z = +1 nucleus ⁹⁴Pd and the role of proton-neutron interactions on the structure of its excited states

Reduced transition probabilities have been extracted between excited, yrast states in the N = Z + 2 nucleus 94Pd. The transitions of interest were observed following decays of the Iπ = 14+ , Ex = 2129-keV isomeric state, which was populated following the projectile fragmentation of a 124Xe primary beam at the GSI Helmholtzzentrum für Schwerionenforschung accelerator facility as part of FAIR Phase-0. Experimental information regarding the reduced E2 transition strengths for the decays of the yrast 8+ and 6+ states was determined following isomer-delayed Eγ1 − Eγ2 − △T2,1 coincidence method, using the LaBr3(Ce)-based FATIMA fast-timing coincidence gamma-ray array, which allowed direct determination of lifetimes of states in 94Pd using the Generalized Centroid Difference (GCD) method. The experimental value for the half-life of the yrast 8+ state of 755(106) ps results in a reduced transition probability of B(E2:8+ →6+ ) = 205+34 −25 e2fm4 , which enables a precise verification of shell-model calculations for this unique system, lying directly between the N = Z line and the N = 50 neutron shell closure. The determined B(E2) value provides an insight into the purity of (g9/2)n configurations in competition with admixtures from excitations between the (lower) N = 3 pf and (higher) N = 4 gds orbitals for the first time. The results indicate weak collectivity expected for near-zero quadrupole deformation and an increasing importance of the T = 0 proton-neutron interaction at N = 48