The eightfold way to dissipation

We provide a complete characterization of hydrodynamic transport consistent with the second law of thermodynamics at arbitrary orders in the gradient expansion. A key ingredient in facilitating this analysis is the notion of adiabatic hydrodynamics, which enables isolation of the genuinely dissipative parts of transport. We demonstrate that most transport is adiabatic. Furthermore, of the dissipative part, only terms at the leading order in gradient expansion are constrained to be sign-definite by the second law (as has been derived before).Comment: 5 pages, 1 figure. v2: minor clarifications. v3: minor changes. title in published version differ

Schwinger-Keldysh formalism II: Thermal equivariant cohomology

Causally ordered correlation functions of local operators in near-thermal quantum systems computed using the Schwinger-Keldysh formalism obey a set of Ward identities. These can be understood rather simply as the consequence of a topological (BRST) algebra, called the universal Schwinger-Keldysh superalgebra, as explained in our companion paper arXiv:1610.01940. In the present paper we provide a mathematical discussion of this topological algebra. In particular, we argue that the structures can be understood in the language of extended equivariant cohomology. To keep the discussion self-contained, we provide a basic review of the algebraic construction of equivariant cohomology and explain how it can be understood in familiar terms as a superspace gauge algebra. We demonstrate how the Schwinger-Keldysh construction can be succinctly encoded in terms a thermal equivariant cohomology algebra which naturally acts on the operator (super)-algebra of the quantum system. The main rationale behind this exploration is to extract symmetry statements which are robust under renormalization group flow and can hence be used to understand low-energy effective field theory of near-thermal physics. To illustrate the general principles, we focus on Langevin dynamics of a Brownian particle, rephrasing some known results in terms of thermal equivariant cohomology. As described elsewhere, the general framework enables construction of effective actions for dissipative hydrodynamics and could potentially illumine our understanding of black holes.Comment: 72 pages; v2: fixed typos. v3: minor clarifications and improvements to non-equilbirum work relations discussion. v4: typos fixed. published versio

Thermal out-of-time-order correlators, KMS relations, and spectral functions

We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in the larger context of out-of-time-ordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with time-reversal to stay within the purview of Schwinger-Keldysh functional integrals, we show that there is a natural way to phrase them directly in terms of OTO correlators. We use these observations to construct a natural causal basis for thermal n-point functions in terms of fully nested commutators. We provide several general results which can be inferred from cyclic orbits of permutations, and exemplify the abstract results using a quantum oscillator as an explicit example.Comment: 36 pages + appendices. v2: minor changes + refs added. v3: minor changes, published versio

Schwinger-Keldysh superspace in quantum mechanics

We examine, in a quantum mechanical setting, the Hilbert space representation of the BRST symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: firstly, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally. Secondly, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.Comment: 30 page

Comments on Hall transport from effective actions

We consider parity-odd transport in 2+1 dimensional charged fluids restricting attention to the class of non-dissipative fluids. We show that there is a two parameter family of such non-dissipative fluids which can be derived from an effective action, in contradistinction with a four parameter family that can be derived from an entropy current analysis. The effective action approach allows us to extract the adiabatic transport data, in particular the Hall viscosity and Hall conductivity amongst others, in terms of the thermodynamic functions that enter as ‘coupling constants’. Curiously, we find that Hall viscosity is forced to vanish, whilst the Hall conductivity is generically a non-vanishing function of thermodynamic data determined in terms of the hydrodynamic couplings

An analysis of ear discharge and antimicrobial sensitivity used in its treatment

Background: Ear discharge is one of the cardinal symptoms of ear infection along with progressive deafness, pain, tinnitus and vertigo. Main objectives of the study were to study the various causes of ear discharge, isolate and identify the microorganisms associated with different causes of ear discharge and study the antibiotic sensitivity patterns of the isolated organisms.Methods: All the patients matching the inclusion criteria were enrolled and sample of ear discharge was collected. This sample was sent to the microbiology laboratory for isolation of microorganism and antimicrobial sensitivity testing.Results: In present study 115 samples of ear discharge were examined for the presence of microorganisms. Out of 115, 93 (80.86%) samples were positive for growth of microorganisms and 22 (19.13%) samples were sterile. Out of 93% positive samples 61 (65.59%) samples were pure-bacterial growth, 8 (*8.60%) samples showed pure fungal growth and 24 (25.80%) showed mixed growth of both bacteria anti fungi.Conclusions: Overall bacterial isolates were higher than fungal and pseudomonas appeared to be most common. It was found sensitive to ceftazidime, amikacin, imipenem, colistin and aztreonam

Safety verification of asynchronous pushdown systems with shaped stacks

In this paper, we study the program-point reachability problem of concurrent pushdown systems that communicate via unbounded and unordered message buffers. Our goal is to relax the common restriction that messages can only be retrieved by a pushdown process when its stack is empty. We use the notion of partially commutative context-free grammars to describe a new class of asynchronously communicating pushdown systems with a mild shape constraint on the stacks for which the program-point coverability problem remains decidable. Stacks that fit the shape constraint may reach arbitrary heights; further a process may execute any communication action (be it process creation, message send or retrieval) whether or not its stack is empty. This class extends previous computational models studied in the context of asynchronous programs, and enables the safety verification of a large class of message passing programs

An analysis of ear discharge and antimicrobial sensitivity to the bacteria used in its treatment

Background: Children are unique population with distinct development and physiological differences from adults, clinical trials in children are essential to develop age-specific, empirically – verified therapies and interventions to determine and improve the best medical treatment available. The aim of this study was to find out the appropriateness and accuracy of the dose of drugs prescribed and compares it with standard dose.Methods: Total 400 prescriptions were collected from the OPD of the paediatrics of Shree Krishna Hospital, Karamsad. Calculation of standard total daily dose for each drug was done by using Clark’s formula and was compared with that of prescribed dose of that particular drug.Results: Total 1042 drugs were prescribed. Among antibiotics (22%) statistically significant difference in the prescribed and standard total daily dose was observed with cefexime [t-value 28.6>1.96 for 95% confidence interval] and metronidazole [t-value2.03>1.96 for 95% confidence interval], NSAIDs (31%), Paracetamol [t-value11.14>1.96 for 95% confidence interval] and antihistaminics (22%), phenylephrine [t-value7.1>1.96 for 95% confidence interval], cetrizine [t-value2.4>2.00 for 95% confidence interval].Conclusions: Results show that prescribed doses of commonly used drugs were higher than the standard dose. This is directly related to the occurrence and severity of adverse drug reactions.