arXiv subjects

Kamal Bhattacharyya

Publications and source records attributed to Kamal Bhattacharyya.

At least 19 recordsLinked to original sources

arXiv2019

Dirichlet eta and beta functions at negative integer arguments: Exact results from anti-limits

A route to evaluate exact sums represented by Dirichlet eta and beta functions, both of which are alternating and divergent at negative integer arguments, is advocated. It rests on precise polynomial extrapolations and stands as a generalization of an early endeavor on lattice sums. Apart from conferring a physical meaning to anti-limits, the scheme advanced here is direct, independent and computationally appealing. A new interpretation of summability is also gained.

math.GM↗

arXiv2019

Improving the Cauchy-Schwarz inequality

We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy-Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in certain singular situations where the celebrated inequality appears to be useless. The basic tenet generates a few other interesting relations, including the improvements over certain common uncertainty bounds. Role of projection operators in modifying the Cauchy-Schwarz relation is noted. Selected applications reveal the efficacy.

quant-ph↗

arXiv2017

Enzyme kinetics: A note on negative reaction constants in Lineweaver-Burk plots

Reaction constants in traditional Michaelis-Menten type enzyme kinetics are most often determined through a linear Lineweaver-Burk plot. While such a graphical plot is sometimes good to achieve the end, it is always better to go for a few numerical tests that can assess the quality of the data set being used and hence offer more reliable measures of the quantities sought, furnishing along with appropriate error estimates. In this context, we specifically highlight how cases may appear with negative reaction constants and explore the origin of such bizarre findings.

physics.chem-ph↗

arXiv2017

How can we distinguish positive cooperativity from auto-catalysis in enzyme kinetics?

Different graphical plots involving the catalytic rate with the (initial) substrate concentration exist in the enzyme kinetics literature to estimate the reaction constants. But, none of these standard plots can unambiguously distinguish between the two important mechanisms of rate enhancement: positive cooperativity among the active sites of an oligomeric enzyme and auto-catalysis of the intermediate complex of an enzyme with a single active site. We achieve this distinction here by providing a nice linear plot for the latter. Importantly, to accomplish this task, no extra information other than the steady-state rate as a function of substrate concentration is required.

physics.chem-ph↗

arXiv2017

A thermodynamic parallel of the Braess road-network paradox

We provide here a thermodynamic analog of the Braess road-network paradox with irreversible engines working between reservoirs that are placed at vertices of the network. Paradoxes of different kinds reappear, emphasizing the specialty of the network.

physics.soc-ph↗

arXiv2016

Uncertainty relations for incompatible observables: Newer results versus modified strategies

Two special situations where the standard uncertainty product inequality appears to be useless are modified. One such case is noted to also trivialize the recently-introduced alternatives [Phys. Rev. Lett. 113, 260401 (2014); Sci. Rep. 6, 23201 (2016)] involving sums of variances. A careful discussion is presented on the experimental justifications of some of the relations [Phys. Rev. A 93, 052108 (2016)] using qutrit and qubit states. Alternative bypass routes are put forward to tackle this situation, with and without involving any auxiliary state. This latter strategy is noted to be vital in an entirely different context concerned with the quality of approximate stationary states. The other case is more frustrating, but an effective method is advanced. En route, the recent alternatives are also simplified to easily accommodate even the cases of more than two observables. In favorable circumstances, an easy option in function space is obtained by virtue of symmetry that does not involve any auxiliary state. Pilot calculations reveal the advantages of our endeavor.

quant-ph↗

arXiv2016

Engine efficiency at maximum power, entropy production and equilibrium thermodynamics

The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary irreversible engine is sometimes believed to behave closely as the Curzon-Ahlborn engine. Efficiency of the latter is obtained commonly by invoking the maximum power principle in a non-equilibrium framework. We outline here two plausible routes within the domain of classical thermodynamics to arrive at the same expression. Further studies on the performances of available practical engines reveal that a simpler approximate formula works much better in respect of bounds to the efficiency. Putting an intermediate-temperature reservoir between the actual source and the sink leads to a few interesting extra observations.

physics.chem-ph↗

arXiv2014

Open chemical reaction networks, steady-state loads and Braess-like paradox

Open chemical reaction systems involve matter-exchange with the surroundings. As a result, species can accumulate inside a system during the course of the reaction. We study the role of network topology in governing the concentration build-up inside a fixed reaction volume at steady state, particularly focusing on the effect of additional paths. The problem is akin to that in traffic networks where an extra route, surprisingly, can increase the overall travel time. This is known as the Braess' paradox. Here, we report chemical analogues of such a paradox in suitably chosen reaction networks, where extra reaction step(s) can inflate the total concentration, denoted as `load', at steady state. It is shown that, such counter-intuitive behavior emerges in a qualitatively similar pattern in networks of varying complexities. We then explore how such extra routes affect the load in a biochemical scheme of uric acid degradation. From a thorough analysis of this network, we propose a functional role of some decomposition steps that can trim the load, indicating the importance of the latter in the evolution of reaction mechanisms in living matter.

physics.chem-ph↗

arXiv2014

States with identical steady dissipation rate: Role of kinetic constants in enzyme catalysis

A non-equilibrium steady state is characterized by a non-zero steady dissipation rate. Chemical reaction systems under suitable conditions may generate such states. We propose here a method that is able to distinguish states with identical values of the steady dissipation rate. This necessitates a study of the variation of the entropy production rate with the experimentally observable reaction rate in regions close to the steady states. As an exactly-solvable test case, we choose the problem of enzyme catalysis. Link of the total entropy production with the enzyme efficiency is also established, offering a desirable connection with the inherent irreversibility of the process. The chief outcomes are finally noted in a more general reaction network with numerical demonstrations.

physics.chem-ph↗

arXiv2013

How is entropy production rate related to chemical reaction rate?

The entropy production rate is a key quantity in irreversible thermodynamics. In this work, we concentrate on the realization of entropy production rate in chemical reaction systems in terms of the experimentally measurable reaction rate. Both triangular and linear networks have been studied. They attain either thermodynamic equilibrium or a non-equilibrium steady state, under suitable external constraints. We have shown that the entropy production rate is proportional to the square of the reaction velocity only around equilibrium and not any arbitrary non-equilibrium steady state. This feature can act as a guide in revealing the nature of a steady state, very much like the minimum entropy production principle. A discussion on this point has also been presented.

physics.chem-ph↗

arXiv2013

Does an irreversible chemical cycle support equilibrium?

The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance condition. In this work, we discuss how the standard theoretical framework can be adapted to include irreversible cycles, avoiding the divergence. With properly redefined force terms, such systems are also seen to reach and sustain equilibria that are characterized by the vanishing of the entropy production rate, though detailed balance is not maintained. Equivalence of the present formulation with Onsager's original prescription is established for both reversible and irreversible cycles, with a few adjustments in the latter case. Further justification of the attainment of true equilibrium is provided with the help of the minimum entropy production principle. All the results are generalized for an irreversible cycle comprising of N number of species.

physics.chem-ph↗

arXiv2013

Accurate estimates of asymptotic indices via fractional calculus

We devise a three-parameter random search strategy to obtain accurate estimates of the large-coupling amplitude and exponent of an observable from its divergent Taylor expansion, known to some desired order. The endeavor exploits the power of fractional calculus, aided by an auxiliary series and subsequent construction of Padé approximants. Pilot calculations on the ground-state energy perturbation series of the octic anharmonic oscillator reveal the spectacular performance.

physics.comp-ph↗

arXiv2013

Enzyme Kinetics: A critique of the quasi-steady-state approximation

The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and hence emergence of the Michaelis-Menten kinetics, with various substrate-enzyme ratios. But, conclusions vary. We solve here the desired set of coupled nonlinear differential equations by invoking a new set of dimensionless variables. Approximate solutions are obtained via the power-series method aided by Pade approximants. The scheme works very successfully in furnishing the initial dynamics at least up to the region where existence of any steady state can be checked. A few conditions for its validity are put forward and tested against the findings. Temporal profiles of the substrate and the product are analyzed in addition to that of the complex to gain further insights into legitimacy of the above approximation. Some recent observations like the reactant stationary approximation and the notions of different timescales are revisited. Signatures of the quasi-steady-state approximation are also nicely detected by following the various reduced concentration profiles in triangular plots. Conditions for the emergence of Michaelis-Menten kinetics are scrutinized and it is stressed how one can get the reaction constants even in the absence of any steady state.

physics.chem-ph↗

arXiv2013

On two classes of perturbations: Role of signs of second-order Rayleigh-Schrödinger energy corrections

We distinguish two extreme classes of perturbation problems depending on the signs of second-order energy corrections and argue why it is generally much more probable to obtain a negative value of the same for any state in the standard Rayleigh-Schrödinger perturbation theory. The classes are seen to differ in reproducing results of finite-dimensional matrix perturbations. A few related issues are also discussed, some of which are based on available analytical results.

quant-ph↗

arXiv2012

A Mixed-Entropic Uncertainty Relation

We highlight the advantages of using simultaneously the Shannon and Fisher information measures in providing a useful form of the uncertainty relation for the position-momentum case. It does not require any Fourier transformation. The sensitivity is also noteworthy.

physics.chem-ph↗

arXiv2012

Single-substrate Enzyme Kinetics: The Quasi-steady-state Approximation and Beyond

We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios to identify the regions of validity of the quasi-steady-state approximation. Certain prevalent conditions are checked and compared against the actual findings. Efficacies of a few other measures are highlighted. Some very recent observations are rationalized, particularly at moderate and high enzyme concentrations.

physics.chem-ph↗

arXiv2009

Are all Quasi-static Processes Reversible?

A process, carried out in a stepwise manner, becomes quasi-static when the number of intermediate steps tends to infinity. Usually, the net entropy production approaches zero under this limiting condition. Hence, such cases are termed reversible. A favorite example is the introduction of an infinite number of intermediate-temperature reservoirs in between the source and the sink for a non-isothermal heat transfer process. We analyze the situation and conclude that such quasi-static processes are not reversible. Indeed, no non-isothermal heat transfer process can ever be made reversible due to an extraneous work term.

physics.chem-ph↗

arXiv2008

Perturbative and non-perturbative studies with the delta function potential

We show that the delta function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential if coupled with a delta function potential remains exactly soluble. We use the strength of the delta function as an expansion parameter and express the second-order energy shift as an infinite sum in perturbation theory. The analytical solution is used to determine the second-order energy shift and hence the sum of an infinite series. By an appropriate choice of the unperturbed system, we can show the importance of the continuum in the energy shift of bound states.

quant-ph↗