Thermodynamic Partition Function Research Articles

Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu–Yang magnetic monopole: Position-dependent mass correspondence and isospectrality

We show that a specific transformation/deformation in a point-like global monopole (PGM) spacetime background would yield an effective position-dependent mass (PDM) Schrödinger equation (i.e., a von Roos PDM Schrödinger equation). We discuss PDM Schrödinger oscillators in a PGM spacetime in the presence of a Wu–Yang magnetic monopole. Within our transformed/deformed global monopole spacetime, we show that all PDM Schrödinger oscillators admit isospectrality and invariance with the constant mass Schrödinger oscillators in the regular global monopole spacetime in the presence of a Wu–Yang magnetic monopole. The exclusive dependence of the thermodynamical partition function on the energy eigenvalues manifestly suggests that the Schrödinger oscillators and the PDM Schrödinger oscillators share the same thermodynamical properties as mandated by their isospectrality. Moreover, we discuss the hard-wall effect on the energy levels of the PDM Schrödinger oscillators in a PGM spacetime without and with a Wu–Yang magnetic monopole. Drastic energy levels’ shift-ups are observed as a consequence of such hard-wall effect.

Information theory and thermodynamic properties of diatomic molecules using molecular potential.

Owing to the devise applications of molecules in industries, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for the position and momentum spaces were obtained to verify the Heisenberg's uncertainty principle. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H2, N2, O2, and HF) using Maple 18 software. The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.

Population Distributions from Native Mass Spectrometry Titrations Reveal Nearest-Neighbor Cooperativity in the Ring-Shaped Oligomeric Protein TRAP.

Allostery pervades macromolecular function and drives cooperative binding of ligands to macromolecules. To decipher the mechanisms of cooperative ligand binding, it is necessary to define, at a microscopic level, the thermodynamic consequences of binding of each ligand to its energetically coupled site(s). However, extracting these microscopic constants is difficult for macromolecules with more than two binding sites, because the observable [e.g., nuclear magnetic resonance (NMR) chemical shift changes, fluorescence, and enthalpy] can be altered by allostery, thereby distorting its proportionality to site occupancy. Native mass spectrometry (MS) can directly quantify the populations of homo-oligomeric protein species with different numbers of bound ligands, provided the populations are proportional to ion counts and that MS-compatible electrolytes do not alter the overall thermodynamics. These measurements can help decipher allosteric mechanisms by providing unparalleled access to the statistical thermodynamic partition function. We used native MS (nMS) to study the cooperative binding of tryptophan (Trp) to Bacillus stearothermophilus trp RNA binding attenuation protein (TRAP), a ring-shaped homo-oligomeric protein complex with 11 identical binding sites. MS-compatible solutions did not significantly perturb protein structure or thermodynamics as assessed by isothermal titration calorimetry and NMR spectroscopy. Populations of Trpn-TRAP11 states were quantified as a function of Trp concentration by nMS. The population distributions could not be explained by a noncooperative binding model but were described well by a mechanistic nearest-neighbor cooperative model. Nonlinear least-squares fitting yielded microscopic thermodynamic constants that define the interactions between neighboring binding sites. This approach may be applied to quantify thermodynamic cooperativity in other ring-shaped proteins.

Black hole entropy, the black hole information paradox, and time travel paradoxes from a new perspective

ABSTRACTRelatively simple but apparently novel ways are proposed for viewing three related subjects: black hole entropy, the black hole information paradox, and time travel paradoxes. (1) Gibbons and Hawking have completely explained the origin of the entropy of all black holes, including physical black holes – nonextremal and in 3-dimensional space – if one can identify their Euclidean path integral with a true thermodynamic partition function (ultimately based on microstates). An example is provided of a theory containing this feature. (2) There is unitary quantum evolution with no loss of information if the detection of Hawking radiation is regarded as a measurement process within the Everett interpretation of quantum mechanics. (3) The paradoxes of time travel evaporate when exposed to the light of quantum physics (again within the Everett interpretation), with quantum fields properly described by a path integral over a topologically nontrivial but smooth manifold.

An action for and hydrodynamics from the improved Large D membrane

It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einstein’s equations. The equation of motion of this membrane is determined by the membrane stress tensor. In this paper we ‘improve’ the membrane stress tensor derived in earlier work to ensure that it defines consistent probe membrane dynamics even at finite D while reducing to previous results at large D. Our improved stress tensor is the sum of a Brown York term and a fluid energy momentum tensor. The fluid has an unusual equation of state; its pressure is nontrivial but its energy density vanishes. We demonstrate that all stationary solutions of our membrane equations are produced by the extremization of an action functional of the membrane shape. Our action is an offshell generalization of the membrane’s thermodynamical partition function. We demonstrate that the thermodynamics of static spherical membranes in flat space and global AdS space exactly reproduces the thermodynamics of the dual Schwarzschild black holes even at finite D. We study the long wavelength dynamics of membranes in AdS space that are everywhere approximately ‘parallel’ to the boundary, and demonstrate that the boundary ‘shadow’ of this membrane dynamics is boundary hydrodynamics with a definite constitutive relation. We determine the explicit form of shadow dual boundary stress tensor upto second order in derivatives of the boundary temperature and velocity, and verify that this stress tensor agrees exactly with the fluid gravity stress tensor to first order in derivatives, but deviates from the later at second order and finite D.

Equilibrium Constants and Rate Constants for Adsorbates: Two-Dimensional (2D) Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models

The thermodynamic state functions and partition functions for adsorbates on solid surfaces are often treated with two-dimensional (2D) ideal gas and 2D ideal lattice gas models. These are idealized limits of the real situation for adsorbates on solid surfaces, which are more accurately described as hindered translators. We describe a simple extension of the ideal 2D gas model to a more realistic ideal hindered translator model based on our recent approximation for the partition function of ideal hindered translators [Sprowl et al., J. Phys. Chem. C., 2016, DOI: 10.1021/acs.jpcc.5b11616]. Expressions for equilibrium constants and rate constants within transition-state theory (TST) are derived in a self-consistent formalism based on both partition functions and standard-state entropies. The mixing of these three adsorbate models (ideal 2D gas, ideal 2D lattice gas, and ideal hindered translator) within the same equilibrium or rate constant calculation is sometimes necessary but requires careful and consiste...

Thermodynamic Partition Function from Quantum Theory for Black Hole Horizons in Loop Quantum Gravity

We establish the link between the thermodynamics and the quantum theory of black hole horizons through the construction of the thermodynamic partition function, partly based on some physically plausible arguments, by beginning from the description of quantum states of the horizon, considering loop quantum gravity (LQG) as the underlying theory. Although the effective “thermalized” form of the partition function has been previously used in the literature to study the effect of thermal fluctuations of the black hole horizon, nonetheless the direct link to any existing quantum theory (which is here taken to be LQG), especially a derivation of the partition function from the quantum states of the horizon, appears to be hitherto absent. This work is an attempt to bridge this small, but essential, gap that appears to be present between the existing literature of quantum theory and thermodynamics of black holes. Furthermore, it may be emphasized that this work isonlyconcerned with themetric independentapproaches to black hole thermodynamics.

Theoretical study of mercury species adsorption mechanism on MnO2(110) surface

Abstract MnO 2 -based sorbents have been considered as potential materials for Hg removal due to their high adsorption ability and high activity in the catalytic oxidation of Hg in coal-fired flue gas. First-principles calculations based on the density functional theory and the periodic slab models were used to gain a fundamental understanding of mercury adsorption mechanism on MnO 2 (1 1 0) surface. The adsorption energies and adsorption structures of mercury species (Hg 0 , HgCl and HgCl 2 ) on MnO 2 (1 1 0) surface were calculated. The electronic structural changes of surface system before and after adsorption were investigated to better understand the surface reactivity. The potential energy diagram of different pathways of mercury species adsorption on surface were given in order to elucidate the mechanism of adsorption process. In addition, thermodynamic data based on statistical thermodynamic partition functions for mercury species adsorption were also calculated. The results show that Hg 0 is strongly adsorbed on MnO 2 (1 1 0) surface with chemisorption. The energy diagrams of HgCl and HgCl 2 adsorption and possible desorption show that HgCl and HgCl 2 can exist stably on the surface because the desorption and dissociation are highly endothermic, yet there is still a possibility that HgCl dissociates and Hg desorbs from the surface. The trends of equilibrium constant suggest that mercury species adsorptions on MnO 2 (1 1 0) surfaces are favorable at low temperature and HgCl 2 is more easily captured than Hg 0 under high temperature.

Anomaly inflow and thermal equilibrium

Using the anomaly inflow mechanism, we compute the flavor/Lorentz non-invariant contribution to the partition function in a background with a U(1) isometry. This contribution is a local functional of the background fields. By identifying the U(1) isometry with Euclidean time we obtain a contribution of the anomaly to the thermodynamic partition function from which hydrostatic correlators can be efficiently computed. Our result is in line with, and an extension of, previous studies on the role of anomalies in a hydrodynamic setting. Along the way we find simplified expressions for Bardeen-Zumino polynomials and various transgression formulae

Chern-Simons terms from thermal circles and anomalies

We compute the full contribution of flavor and (or) Lorentz anomalies to the thermodynamic partition function. Apart from the Wess-Zumino consistency condition the Euclidean generating function must satisfy an extra requirement which we refer to as `consistency with the Euclidean vacuum.' The latter requirement fixes all Chern-Simons terms that arise in a particular Kaluza-Klein reduction of the theory. The solution to both conditions may be encoded in a `thermal anomaly polynomial' which we compute. Our construction fixes all the thermodynamic response parameters of a hydrodynamic theory associated with anomalies.

Enzymatic Detoxication, Conformational Selection, and the Role of Molten Globule Active Sites

The role of conformational ensembles in enzymatic reactions remains unclear. Discussion concerning "induced fit" versus "conformational selection" has, however, ignored detoxication enzymes, which exhibit catalytic promiscuity. These enzymes dominate drug metabolism and determine drug-drug interactions. The detoxication enzyme glutathione transferase A1-1 (GSTA1-1), exploits a molten globule-like active site to achieve remarkable catalytic promiscuity wherein the substrate-free conformational ensemble is broad with barrierless transitions between states. A quantitative index of catalytic promiscuity is used to compare engineered variants of GSTA1-1 and the catalytic promiscuity correlates strongly with characteristics of the thermodynamic partition function, for the substrate-free enzymes. Access to chemically disparate transition states is encoded by the substrate-free conformational ensemble. Pre-steady state catalytic data confirm an extension of the conformational selection model, wherein different substrates select different starting conformations. The kinetic liability of the conformational breadth is minimized by a smooth landscape. We propose that "local" molten globule behavior optimizes detoxication enzymes.

THERMODYNAMIC BEHAVIOUR OF HYPERSENSITIVE TRANSITION OBSERVED IN SOME THULIUM ION DOPED SYSTEMS

The Tm(III) doped systems with various ligands studied with respect to hypersensitive transition. The spectroscopic data for hypersensitive transition have been correlated with the thermodynamic parameters. The thermodynamic parameters include thermodynamic efficiency and partition function of the transition.

Q-boson coherent states and para-Grassmann variables for multi-particle states

We describe coherent states and associated generalized Grassmann variables for a system of m independent q-boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus. Formulae for operator traces are given and the thermodynamic partition function for a system of q-boson oscillators is discussed.

Thermodynamics of superstring on near-extremal NS5 and effective Hagedorn behavior

We study the thermodynamical torus partition function of superstring on the near-extremal black NS5-brane background. The exact partition function has been computed with the helps of our previous works:[arXiv:1012.5721 [hep-th]], [arXiv:1109.3365 [hep-th]], and naturally decomposed into two parts. The first part is contributed from strings freely propagating in the asymptotic region, which are identified as the superstring gas at the Hawking temperature on the linear-dilaton background. The second part includes the contribution localized around the `tip of cigar', which characterizes the non-extremality. Remarkably, the latter part includes massless excitations with non-vanishing thermal winding, which signifies that the Hagedorn-like behavior effectively appears, even though the Hawking temperature is much lower than the Hagedorn temperature. We also explore the high-temperature backgrounds defined by the orbifolding along the Euclidean time direction. In those cases, the thermal winding modes localized around the tip are found to be tachyonic, reflecting the singularities of Euclidean backgrounds caused by orbifolding.

Accelerating the Convergence and Reducing the Variance of Path Integral Calculations of Quantum Mechanical Free Energies by Using Local Reference Potentials

We present two new methods to accelerate the convergence of Feynman path integral calculations of thermodynamic partition functions. The first enhancement uses information from instantaneous normal mode (INM) calculations to decrease the number of discretized points necessary to represent the Feynman paths and is denoted the local generalized Pitzer-Gwinn (LGPG) scheme. The second enhancement, denoted harmonically guided variance reduction (HGVR), reduces the variance in Monte Carlo (MC) calculations by exploiting the correlation between the sampling error associated with the sum over paths at a particular centroid location for the accurate potential and for the INM approximation of a model potential, the latter of which can be exactly calculated. The LGPG scheme can reduce the number of quadrature points required along the paths by nearly an order of magnitude, and the HGVR scheme can reduce the number of MC samples needed to achieve a target accuracy by more than an order of magnitude. Numerical calculations are presented for H2O2, a very anharmonic system where torsional motion is important, and H2O, a system more amenable to harmonic reference treatment.

The lysogeny/lysis switch and entropies of stationary states in λ phage

The system of Escherichia coli infected by λ phage is one of the templates for quantitative study of regulated networks. In this article, according to the characteristics of the interactions between operators and regulators, the probabilities of regulators binding to operators are described by thermodynamic partition function. On the basis of bifurcation analysis of this regulated network, the entropies of stationary states are calculated. Results show that the entropies of both lysogenic state and lytic state are lower than those of saddle-point and bifurcation point states. Moreover, we find that the lysogenic state has lower entropy than lytic state, which proves that the lysogenic state has a higher biological order.

New Method for Sequence Alignment Based on Probabilities of Nucleotide Correspondences

ABSTRACTThe objective of our work is to develop a general method for structurally related, but diverged sequences for simultaneous optimization of alignment and self-folding—the so-called Sankoff's program for simultaneous prediction of secondary structure and alignment between nucleotide sequences. A simple reason behind the simultaneous optimization of alignment and self-folding is that strong structural consensus among related, but diverged sequences are a good indicator for preserved functional role. Up to now there is no a general solution for this long standing problem.Here we discuss an approach which is just a first step to the full realization of Sankoff's program. Currently available models and software packages, such as foldalign, dynalign and others, implement only restricted versions (variations around first align and then fold or oppositely) of Sunkoff's program and do not use the full loop-based RNA/DNA energy model.We divided Sankof's program in two steps based on the analogy between the classical alignment algorithm and hybridization without self-folding. The next step is to include in the alignment an algorithm for the self-folding. In our approach, the alignment problem requires the implementation of the full loop-based RNA/DNA energy model for hybridization of two sequences. For this, we divided the alignment between two sequences into loops and associated a score to each loop in such way that the total score of the alignment is a sum over the scores for each alignment loop. The loop scoring model for alignment consists of following loop types: stacking with matched and mismatched pairs, bulges, internal loops and dangling ends.Calculation of thermodynamic partition function over all possible double-stranded conformations is interpreted in terms of all possible canonical pairwise alignments. The partition function is computed by means of a dynamic programming algorithm and used to determine the probability of an alignment as well as the probability of each possible match between two sequence positions. For calculation of match probabilities detailed recursion relations for partition functions of alignments are based on their recursion analogs for hybridization of subsequences. The partition function is used for backtracking and reconstructing a properly weighted ensemble of optimal and suboptimal alignments.

Quantum-to-classical correspondence and Hubbard-Stratonovich dynamical systems: A Lie-algebraic approach

We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first part of the paper utilizes a geometric Hilbert-space-invariant formulation of unitary time-evolution, where a quantum Hamiltonian is viewed as a trajectory in an abstract Lie algebra, while the sought-after evolution operator is a trajectory in a dynamic group, generated by the algebra via exponentiation. The evolution operator is uniquely determined by the time-dependent dual generators that satisfy a system of differential equations, dubbed here dual Schrodinger-Bloch equations, which represent a viable alternative to the conventional Schrodinger formulation. These dual Schrodinger-Bloch equations are derived and analyzed on a number of specific examples. It is shown that deterministic dynamics of a closed classical dynamical system occurs as action of a symmetry group on a classical manifold and is driven by the same dual generators as in the corresponding quantum problem. This represents quantum-to-classical correspondence. In the second part of the paper, we further extend the Lie algebraic approach to a wide class of interacting many-particle lattice models. A generalized Hubbard-Stratonovich transform is proposed and it is used to show that the thermodynamic partition function of a generic many-body quantum lattice model can be expressed in terms of traces of single-particle evolution operators governed by the dynamic Hubbard-Stratonovich fields. Finally, we derive Hubbard-Stratonovich dynamical systems for the Bose-Hubbard model and a quantum spin model and use the Lie-algebraic approach to obtain new non-perturbative dual descriptions of these theories.

Nonperturbative quantum dynamics of the order parameter in the BCS pairing model

We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different Hilbert spaces of single-particle and paired/empty states. This allows us to factorize the full thermodynamic partition function into a combination of simple terms associated with real spins on singly-occupied states and the partition function of the quantum XY-model for Anderson pseudospins associated with the paired/empty states. Using coherent-state path-integral, we calculate the effects of superconducting phase fluctuations exactly. The contribution of superconducting amplitude fluctuations to the partition function in the broken-symmetry phase is shown to follow from the Bogoliubov-de Gennes equations in imaginary time. These equations in turn allow several interesting mappings, e.g., they are shown to be in a one-to-one correspondence with the one-dimensional Schr\"odinger equation in supersymmetric Quantum Mechanics. However, the most practically useful approach to calculate functional determinants is found to be via an analytical continuation of the quantum order parameter to real time, \Delta(\tau -> it), such that the problem maps onto that of a driven two-level system. The contribution of a particular dynamic order parameter to the partition function is shown to correspond to the sum of the Berry phase and dynamic phase accumulated by the pseudospin. We also examine a family of exact solutions for two-level-system dynamics on a class of elliptic functions and suggest a compact expression to estimate the functional determinants on such trajectories. The possibility of having quantum soliton solutions co-existing with classical BCS mean-field is discussed.

Thermodynamics and quark susceptibilities: A Monte Carlo approach to the Polyakov–Nambu–Jona-Lasinio model

The Monte-Carlo method is applied to the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. This leads beyond the saddle-point approximation in a mean-field calculation and introduces fluctuations around the mean fields. We study the impact of fluctuations on the thermodynamics of the model, both in the case of pure gauge theory and including two quark flavors. In the two-flavor case, we calculate the second-order Taylor expansion coefficients of the thermodynamic grand canonical partition function with respect to the quark chemical potential and present a comparison with extrapolations from lattice QCD. We show that the introduction of fluctuations produces only small changes in the behavior of the order parameters for chiral symmetry restoration and the deconfinement transition. On the other hand, we find that fluctuations are necessary in order to reproduce lattice data for the flavor non-diagonal quark susceptibilities. Of particular importance are pion fields, the contribution of which is strictly zero in the saddle point approximation.