The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping

We propose a mathematical formulation of the zeroth law of thermodynamics and develop a stochastic dynamical theory, with a consistent irreversible thermodynamics, for systems possessing sustained conservative stationary current in phase space while in equilibrium with a heat bath. The theory generalizes underdamped mechanical equilibrium: $dx=gdt+\{-D\nabla\phi dt+\sqrt{2D}dB(t)\}$, with $\nabla\cdot g=0$ and $\{\cdots\}$ respectively representing phase-volume preserving dynamics and stochastic damping. The zeroth law implies stationary distribution $u^{ss}(x)=e^{-\phi(x)}$. We find an orthogonality $\nabla\phi\cdot g=0$ as a hallmark of the system. Stochastic thermodynamics based on time reversal $\big(t,\phi,g\big)\rightarrow\big(-t,\phi,-g\big)$ is formulated: entropy production $e_p^{\#}(t)=-dF(t)/dt$; generalized "heat" $h_d^{\#}(t)=-dU(t)/dt$, $U(t)=\int_{\mathbb{R}^n} \phi(x)u(x,t)dx$ being "internal energy", and "free energy" $F(t)=U(t)+\int_{\mathbb{R}^n} u(x,t)\ln u(x,t)dx$ never increases. Entropy follows $\frac{dS}{dt}=e_p^{\#}-h_d^{\#}$. Our formulation is shown to be consistent with an earlier theory of P. Ao. Its contradistinctions to other theories, potential-flux decomposition, stochastic Hamiltonian system with even and odd variables, Klein-Kramers equation, Freidlin-Wentzell's theory, and GENERIC, are discussed.Comment: 25 page

Geometric Phase, Hannay's Angle, and an Exact Action Variable

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.Comment: Submitted to Phys. Rev. Lett. (revised version

CO adsorption on Cu(111) and Cu(001) surfaces: improving site preference in DFT calculations

CO adsorption on Cu(111) and Cu(001) surfaces has been studied within ab-initio density functional theory (DFT). The structural, vibrational and thermodynamic properties of the adsorbate-substrate complex have been calculated. Calculations within the generalized gradient approximation (GGA) predict adsorption in the threefold hollow on Cu(111) and in the bridge-site on Cu(001), instead of on-top as found experimentally. It is demonstrated that the correct site preference is achieved if the underestimation of the HOMO-LUMO gap of CO characteristic for DFT is correct by applying a molecular DFT+U approach. The DFT+U approach also produces good agreement with the experimentally measured adsorption energies, while introducing only small changes in the calculated geometrical and vibrational properties further improving agreement with experiment which is fair already at the GGA level.Comment: 15 pages, 3 figures, submitted to Surf. Sci., WWW: http://cms.mpi.univie.ac.at/mgajdos

A national population-based cohort study to investigate inequalities in maternal mortality in the UK 2009-17

Background: Disparities have been documented in maternal mortality rates between women from different ethnic, age and socio-economic groups in the UK. It is unclear whether there are differential changes in these rates amongst women from different groups over time. The objectives of this analysis were to describe UK maternal mortality rates in different age, ethnic and socio-economic groups between 2009 and 2017, and to identify whether there were changes in the observed inequalities, or different trends amongst population subgroups. Methods: Maternal mortality rates with 95% confidence intervals (CI) in specific age, deprivation and ethnic groups were calculated using numbers of maternal deaths as numerator and total maternities as denominator. Relative risks (RR) with 95% CI were calculated and compared using ratios of relative risk. Change over time was investigated using non-parametric tests for trend across ordered groups. Results: Women from black and Asian groups had a higher mortality rate than white women in most time periods, as did women aged 35 and over and women from the most deprived quintile areas of residence. There was evidence of an increasing trend in maternal mortality amongst black women and a decrease in mortality amongst women from the least deprived areas, but no trends over time in any of the other ethnic, age or IMD groups were seen. There was a widening of the disparity between black and white women (RR 2.59 in 2009-11 compared with 5.27 in 2015-17, ratio of the relative risks 2.03, 95% CI 1.11, 3.72). Conclusions: The clear differences in the patterns of maternal mortality amongst different ethnic, age and socio-economic groups emphasise the importance of research and policies focussed specifically on women from black and minority ethnic groups, together with other disadvantaged groups, to begin to reduce maternal mortality in the UK.</p

Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

Relationship between Thermodynamic Driving Force and One-Way Fluxes in Reversible Chemical Reactions

Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a theorem that relates forward and re-verse fluxes and free energy for any chemical process operating in a steady state. This rela-tionship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state, provides a novel equivalent definition for chemical reaction free energy. In addition, it is shown that previously unrelated theories introduced by Ussing and Hodgkin and Huxley for transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks for entropy production in microscopically reversible systems, are united in a common framework based on this relationship.Comment: 11 page

Time evolution, cyclic solutions and geometric phases for the generalized time-dependent harmonic oscillator

The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and geometric phases. In this approach, finding the time evolution operator for the Schr\"odinger equation is reduced to solving an ordinary differential equation for a c-number vector which moves on a hyperboloid in a three-dimensional space. Cyclic solutions do not exist for all time intervals. A necessary and sufficient condition for the existence of cyclic solutions is given. There may exist some particular time interval in which all solutions with definite parity, or even all solutions, are cyclic. Criterions for the appearance of such cases are given. The known relation that the nonadiabatic geometric phase for a cyclic solution is proportional to the classical Hannay angle is reestablished. However, this is valid only for special cyclic solutions. For more general ones, the nonadiabatic geometric phase may contain an extra term. Several cases with relatively simple Hamiltonians are solved and discussed in detail. Cyclic solutions exist in most cases. The pattern of the motion, say, finite or infinite, can not be simply determined by the nature of the Hamiltonian (elliptic or hyperbolic, etc.). For a Hamiltonian with a definite nature, the motion can changes from one pattern to another, that is, some kind of phase transition may occur, if some parameter in the Hamiltonian goes through some critical value.Comment: revtex4, 28 pages, no figur

Synaptic inhibition in the lateral habenula shapes reward anticipation

The lateral habenula (LHb) supports learning processes enabling the prediction of upcoming rewards. While reward-related stimuli decrease the activity of LHb neurons, whether this anchors on synaptic inhibition to guide reward-driven behaviors remains poorly understood. Here, we combine in vivo two-photon calcium imaging with Pavlovian conditioning in mice and report that anticipatory licking emerges along with decreases in cue-evoked calcium signals in individual LHb neurons. In vivo multiunit recordings and pharmacology reveal that the cue-evoked reduction in LHb neuronal firing relies on GABAA-receptor activation. In parallel, we observe a postsynaptic potentiation of GABAA-receptor-mediated inhibition, but not excitation, onto LHb neurons together with the establishment of anticipatory licking. Finally, strengthening or weakening postsynaptic inhibition with optogenetics and GABAA-receptor manipulations enhances or reduces anticipatory licking, respectively. Hence, synaptic inhibition in the LHb shapes reward anticipation. Keywords: GABA(A) receptors; cue-reward associative behavior; lateral habenula; synaptic inhibition; synaptic plasticit