Covariant statistical mechanics and the stress-energy tensor

After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a non-vanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector \beta. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector \beta, i.e. T^{\mu \nu} = - \partial \Phi^\mu/\partial \beta_\nu. This formula establishes a relation between stress-energy tensor and entropy current at equilibrium possibly extendable to non-equilibrium hydrodynamics.Comment: 4 pages. Final version accepted for publication in Phys. Rev. Let

Synthesis and viscosity behavior of poly(γ-p-biphenylmethyl-L-glutamate) in benzene/dichloroacetic acid mixtures, a comparison with poly(γ-benzyl-L-glutamate)

The synthesis of poly(γ-p-biphenylmethyl-L-glutamate), PBPLG, (poly{L-imino-1-[2-(4-biphenylylmethoxycarbonyl)ethyl]-2-oxoethylene}), (1d) is described. The viscosity behavior of this polymer in benzene/dichloroacetic acid mixtures (c=0,2.10 -3 - 1,4.10 -3 g/cm3) at 25°CC is investigated. The results are compared with measurements on poly(γ-benzyl-L-glutamate), PBLG, (poly[L-imino-1-(2-benzyloxycarbonylethyl)-2-oxoethylene]), (1c) under the same conditions. A transition from a rigid hydrogen bonded helix to a random solvated coil occurs in two stages for both: PBPLG (first stage 0-55%, second stage 55-100% dichloroacetic acid) and PBLG (first stage 0-70%, second stage 70-100% dichloroacetic acid). \ud Therefore, the introduction of a p-phenyl substituent in PBLG leads to a less stable helix in benzene/dichloroacetic acid mixtures. \ud The stability and viscosity behavior of PBLG in benzene/dichloroacetic acid mixtures (c=0,2.10 - 3 - 1,4.10 - 3g/cm3) is quite similar to the behavior of PBLG in m-cresol/dichloroacetic acid mixtures (c=1,0.10 - 3 - 4,0.10 - 3 g/cm3)

More Bang for Your Buck: Improved use of GPU Nodes for GROMACS 2018

We identify hardware that is optimal to produce molecular dynamics trajectories on Linux compute clusters with the GROMACS 2018 simulation package. Therefore, we benchmark the GROMACS performance on a diverse set of compute nodes and relate it to the costs of the nodes, which may include their lifetime costs for energy and cooling. In agreement with our earlier investigation using GROMACS 4.6 on hardware of 2014, the performance to price ratio of consumer GPU nodes is considerably higher than that of CPU nodes. However, with GROMACS 2018, the optimal CPU to GPU processing power balance has shifted even more towards the GPU. Hence, nodes optimized for GROMACS 2018 and later versions enable a significantly higher performance to price ratio than nodes optimized for older GROMACS versions. Moreover, the shift towards GPU processing allows to cheaply upgrade old nodes with recent GPUs, yielding essentially the same performance as comparable brand-new hardware.Comment: 41 pages, 13 figures, 4 tables. This updated version includes the following improvements: - most notably, added benchmarks for two coarse grain MARTINI systems VES and BIG, resulting in a new Figure 13 - fixed typos - made text clearer in some places - added two more benchmarks for MEM and RIB systems (E3-1240v6 + RTX 2080 / 2080Ti

Growth and Inequality: A Meta-Analysis

In recent years there has been a growing interest in the impact of inequality on economic growth. Both theoretical and empirical approaches have produced ambiguous results on sign and size of this relationship. Although there is a considerable part of the literature that considers inequality detrimental to growth, more recent studies have challenged this result and found a positive effect of inequality on growth. This paper contributes to the debate by using meta-analytical techniques to describe variation in observed outcomes of the empirical studies and to identify sources of variation

Speed limits for quantum gates in multi-qubit systems

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.Comment: 7 pages (two-column), 2 figures, 2 table

Dissipative hydrodynamics in 2+1 dimension

In 2+1 dimension, we have simulated the hydrodynamic evolution of QGP fluid with dissipation due to shear viscosity. Comparison of evolution of ideal and viscous fluid, both initialised under the same conditions e.g. same equilibration time, energy density and velocity profile, reveal that the dissipative fluid evolves slowly, cooling at a slower rate. Cooling get still slower for higher viscosity. The fluid velocities on the otherhand evolve faster in a dissipative fluid than in an ideal fluid. The transverse expansion is also enhanced in dissipative evolution. For the same decoupling temperature, freeze-out surface for a dissipative fluid is more extended than an ideal fluid. Dissipation produces entropy as a result of which particle production is increased. Particle production is increased due to (i) extension of the freeze-out surface and (ii) change of the equilibrium distribution function to a non-equilibrium one, the last effect being prominent at large transverse momentum. Compared to ideal fluid, transverse momentum distribution of pion production is considerably enhanced. Enhancement is more at high $p_T$ than at low $p_T$. Pion production also increases with viscosity, larger the viscosity, more is the pion production. Dissipation also modifies the elliptic flow. Elliptic flow is reduced in viscous dynamics. Also, contrary to ideal dynamics where elliptic flow continues to increase with transverse momentum, in viscous dynamics, elliptic flow tends to saturate at large transverse momentum. The analysis suggest that initial conditions of the hot, dense matter produced in Au+Au collisions at RHIC, as extracted from ideal fluid analysis can be changed significantly if the QGP fluid is viscous.Comment: 11 pages, 10 figures (revised). In the revised version, calculations are redone with ADS/CFT and perurbative estimate of viscosity. Comments on the unphysical effects like early reheating of the fluid, in 1st order dissipative theories are added. The particle spectra calculations are redone with modified programm