Entropy Exchange Research Articles

The heats of exchange of transition metal ions on the Na form of clinoptilolite

Direct calorimetric measurements were used to determine the heats of exchange of the Mn2+, Co2+, Cu2+, and Ni2+ cations on the Na form of clinoptilolite over the entire range of solid phase fillings with sorbed cations. In parallel, ion exchange isotherms for the systems were measured by the sorption-analytic method. The integral free energies and entropies of ion exchange were calculated. It was shown that the solution phase of the clinoptilolite-electrolyte solution two-phase system contributed significantly to the total thermodynamic characteristics of ion exchange. The differentiation of the dependence of the integral enthalpy on the degree of filling was performed to show that the clinoptilolite structure contained at least two types of exchange sites having different interaction energies with transition metal ions.

Modeling Non-Equilibrium Dynamics of a Discrete Probability Distribution: General Rate Equation for Maximal Entropy Generation in a Maximum-Entropy Landscape with Time-Dependent Constraints

A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.

Extensions of the quantum Fano inequality

Quantum Fano inequality (QFI) in quantum information theory provides an upper bound to the entropy exchange by a function of the entanglement fidelity. We give various Fano-like upper bounds to the entropy exchange and QFI is a special case of these bounds. These bounds also give an alternate derivation of the QFI.

Entropy Exchange and Entanglement in Superconducting Charge Qubit Inside a Resonant Cavity with Intrinsic Decoherence

By considering the intrinsic decoherence effect, we investigate the entropy exchange and entanglement in the interacting system of a superconducting charge qubit coupled to a single-mode optical cavity. We found that although the intrinsic decoherence leads to an irreversible evolution of the interacting system due to a suppression of coherent quantum features through the decay of off-diagonal matrix elements of the density operator, and has an apparently influence on the partial entropies of the two-component subsystems, it dose not destroy entropy exchange behavior. In addition, the lower bound of the concurrence, as the measure of entanglement of the coupling system, is calculated. It is shown that the evolution of entanglement is sensitive to the change of the intrinsic decoherence.

Entropy exchange in laser cooling

It is usually presumed that spontaneous emission is necessary to remove the entropy lost by laser-cooled atoms. Here we show that the changes in the laser beams themselves constitute a sufficiently large reservoir of $N$ states accessible to the system that their entropy $S={k}_{B}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(N)$ is sufficient to absorb the entropy lost by the atoms in the cooling process. Proper choice of laser parameters could possibly produce cooling of atoms or molecules over a wide range of temperatures without spontaneous emission.

Thermodynamics of ion exchange in a sulfonated polymer based on cis-tetraphenylmetacyclophanoctol

The thermodynamic characteristics of proton exchange in SO3H groups of a sulfonated network polymer based on cis-tetraphenylmetacyclophanoctol for Na+, Cu2+ cations from aqueous solutions were considered for the first time. Microcalorimetric measurements of the heat effects of Na+-H+ and Cu2+-H+ exchanges were performed, equilibrium compositions of polymer and solution were determined. The changes of Gibbs energy, enthalpy and entropy of ion exchange were calculated.

The entropy matrix generated exergy model for a Photovoltaic heat exchanger under critical operating conditions

The maximum entropy generation approach is adopted to develop the exergy model for a Photovoltaic (PV) heat exchanger with vertical heat exchange sections under critical operation of buoyancy-induced hybrid airflow. The Photovoltaic (PV) heat exchanger was constructed with two adjacent Photovoltaic (PV) modules with double-glass faces and back panel and assembled on a wooden duct and framing structure. The entropy matrix is formulated for performing conjugate entropy exchange calculations with convective, conductive and radiation exchange of entropies. The model is developed and validated with complementary measurements obtained from the experimental apparatus setup in an outdoor test room facility at Concordia University, Montreal, Canada.

Plant transpiration and net entropy exchange on the Earth’s surface in a Czech watershed

The influence of plant transpiration on the entropy exchange was quantified as associated with the degradation of solar energy on the Earth’s surface covered by plants. Two surfaces were studied: (1) productive surface — plant transpiration taken as equal to the potential one, (2) non-productive surface — plant transpiration taken as equal to zero. The entropy exchanges associated with the absorption of solar radiation and with the conversion of absorbed solar radiation into the sensible heat and latent heat were taken into account. These processes were examined in the experimental watershed Liz (828–1074 m a.s.l.) located in the Bohemian Forest (Czech Republic). We found that in the growing season 1992 the net entropy exchange in humid hydrologic period (the Earth’s surface is productive) was considerably higher than in the arid one (the Earth’s surface was productive in 39% of days, and non-productive in 61% of days). Considering that the biotic effect on the Earth’s functioning can be measured with the help of the net entropy exchange, we can assume that the theory that biotic activities — represented by plant transpiration here — are the cause of the self-organizing processes in Earth’s environment is proved in the watershed scale.

Entropy exchange, coherent information, and concurrence

For a simple model we derive analytic expressions of entropy exchange and coherent information, from which relations between them and the concurrence are drawn. We find that in the quantum evolution the entropy exchange exhibits behavior opposite to that of the concurrence, whereas the coherent information shows features very similar to those of the concurrence. The meaning of this result for general systems is discussed.

Tracing the Second Law

This article reviews the evolution in the field of thermodynamics. In the 19th century, James Joule, an English physicist, discovered the equivalence of heat and work, and the First Law of Thermodynamics was firmly established. The Second Law developed in phases over some 125 years. It is one of the most abstract laws of physical science and is the bane of students and others who try to understand its complexity. The first phase in the evolution of the Second Law is older than Joule's work and is due to Sadi Carnot. Carnot published his results in a book, Reflections on the Motive Power of Fire, in 1824. The second phase in the evolution of the Second Law took place in 1849, when William Thomson studied Carnot's work. The third phase of the evolution of the Second Law was carried out by a German professor of mathematical physics, Rudolf Clausius, who became aware of the work of Carnot, Joule, and Kelvin in 1850. A fourth phase in the development of the Second Law was carried out by Lars Onsager in 1931. The fifth phase in the evolution of the Second Law was developed by Ilya Prigogine in 1945. The Second Law is a statement that the entropy content of a system may be increased or decreased by entropy exchanges with the environment, but may only be increased as irreversibilities cause entropy creation.

The thermodynamic characteristics of ion exchange in a sulfonated polymer based on cis-tetraphenylcalix[4]resorcinarene

The selectivity and thermodynamic characteristics of exchange of protons in SO3H groups of a sulfonated network polymer based on cis-tetraphenylcalix[4]resorcinarene for Na+, Cu2+, and In3+ cations from aqueous solutions are considered. Semiempirical quantum-chemical calculations of molecular ensembles modeling the structure of the elementary polymer unit in the H and Na forms were performed. The experimental data on the equilibrium phase compositions and the heat of exchange were used to calculate the thermodynamic equilibrium constants, Gibbs energy, enthalpy, and entropy of ion exchange.

Optimality of private quantum channels

We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel and the von Neumann entropy of the ciphertext state ϱ(0). Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if they exist) optimizes the entropy. For non-ancillary single-qubit PQC we have derived the optimal entropy for the arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analysed all the possible single-qubit private quantum channels for an arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.

Order and anti-order in olivine III: Variation of the cation distribution in the Fe,Mg olivine solid solution series with temperature and composition

The structures of four Fe,Mg olivine crystals Fa11.6, Fa22.3, Fa27.6 and Fa27.8 have been investigated by ex situ and in situ experiments using single-crystal X-ray diffractometry. For the ex situ experiments, the crystals were quenched after equilibration at temperatures between 500 °C and 900 °C. Resetting effects were only observed for samples quenched from 900 °C. The in situ experiments were performed at temperatures up to 750 °C. With increasing equilibration temperature, Fe 2+ was found to progressively segregate into the octahedral M1 site, i.e. the degree of anti-order increases with rising temperature. Thus, contrary to the results of Rinaldi et al. (2000) and Redfern et al. (2000), no indication of an ordering reversal at high temperatures is found. Incorporation of the results of Heinemann et al. (2006) on olivine Fa47.9 into the present study allows for the first time to systematically investigate the compositional variation of the temperature dependence of the Fe 2+ ,Mg site occupancies. The formulation of Thompson (1969, 1970) for solid solutions undergoing non-convergent disordering processes, (1) \[{-} RTln K_{D} = [{\Delta}H_{exch}^{0} {-} (L_{M1}^{H} {-} L_{M2}^{H})X] {-} T[{\Delta}S_{exch}^{0} {-} (L_{M1}^{S} {-} L_{M2}^{S})X],\] yielded \begin{eqnarray*}&&{\Delta}H_{exch}^{0} = 1153 ({\pm}67) J/mol{ }{ }{\Delta}S_{exch}^{0} = 3.743({\pm}0.072) J/molK\\&&L_{M1}^{H} {-} L_{M2}^{H} = 973 ({\pm}211) J/mol{ }{ }L_{M1}^{S} {-} L_{M2}^{S} = {-} 0.89 ({\pm}0.24) J/molK.\end{eqnarray*} ΔH exch 0 and ΔS exch 0 are the exchange enthalpy and entropy, respectively, related to the Fe 2+ ,Mg site exchange, L M1,M2 H and L M1,M2 S denote enthalpic and entropic intrasite interaction parameters. The compositional parameter X varies between −1 for forsterite (Fa0) and +1 for fayalite (Fa100). The magnitudes and signs of the four refined quantities can be rationalized in terms of thermodynamic and crystal-chemical considerations. (L M1 H − L M2 H ) > 0 indicates that the interactions between the M1 sites are stronger than those between the M2 sites, conforming with the M1-M1 distances being shorter than the M2-M2 distances. (L M1 S − L M2 S ) exch 0 increases towards the Mg endmember while ΔS exch 0 decreases. Since ΔH exch 0 > 0 stabilizes the ordered state whereas ΔS exch 0 >0 stabilizes the anti-ordered state, it follows that the ordered state is progressively favoured with increasing Mg content. Consequently, ordered site distributions should occur only in slowly cooled Mg-rich olivines, whereas olivines with Fa > 25 mol% should be found in their anti-ordered states frozen during cooling. This conclusion is supported by structure refinements and ordering path simulations for a metamorphic olivine Fa12.4 as well as two volcanic olivines Fa25.6 and Fa27.8.

A study of some equation‐of‐state parameters of poly(methylhydrosiloxane‐co‐dimethylsiloxane) with some solvents by gas chromatography

AbstractTrace amount of methyl acetate, ethyl acetate, tert‐butyl acetate, pentane, hexane, and heptane were passed through the chromatographic column loaded with poly(methylhydrosiloxane‐co‐dimethylsiloxane) coated on Chromosorb W. The retention diagrams of the solvents on the copolymer were plotted by means of specific retention volumes at temperatures between 40 and 80°C by inverse gas chromatography technique. In this study, some thermodynamic interaction parameters such as Flory–Huggins polymer–solvent interaction parameter, equation‐of‐state polymer–solvent interaction parameter, effective exchange energy parameter, and weight fraction activity coefficients at infinite dilution of the solvent were determined. Then, the exchange enthalpy parameter and entropy parameter were determined by using a relation for the enthalpy interaction parameter of the equation‐of‐state theory, which is arranged for the inverse gas chromatography conditions. Later, the partial molar heat of sorption and the partial molar heat of mixing were obtained. The solubility parameter of this copolymer was determined as 6.64 (cal/cm3)1/2 at room temperature. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1627–1631, 2007

Entropy exchange and entanglement of an in motion two-level atom with a quantized field

The entanglement dynamics in an atom–field interacting system is investigated by considering both the atomic motion and the field-mode structure. Entropy exchange, which is regarded in recent years as a form of anti-correlated behavior between the field and the atomic subsystems (Boukobza E, Tannor DJ. Phys Rev A 2005;71:063821), is explored. The relationship between entropy correlations and entanglement is discussed. Agreement with the measure of entanglement of the coupling system is found. Our results show that the behavior of the entropy exchange is not dependent on the atomic motion and the field-mode structure.

Equilibria and heats of ion exchange in the system of mordenite-alkali and alkaline earth cations

A concurrent absorption analytical study of the ion exchange equilibria and direct microcalorimetric measurement of the heat of ion exchange absorption of K+ and Ca2+ cations for the sodium forms of two mordenites (NaM) obtained from naturally occurring samples rich in Na+ and Ca2+ cations has been carried out for the first time. The free energies and entropies of exchange have been calculated. It was shown that the free energy of exchange in the K+-NaM system is determined by the enthalpy, whereas in the Ca2+-NaM system it is determined by the entropy of solvation. The measured thermodynamic characteristics of exchange were analyzed taking into account the preferred localization of sorption for the cations in the structure. A memory effect in natural mordenites has been established for extra-skeletal K+ and Ca2+ cations, in the presence of which these zeolites crystallized in nature.

Continuous variable entanglement in the system of a mesoscopic Josephson junction with a thermal cavity field

The dynamical behavior of entanglement for the system of a mesoscopic Josephson junction coupled to a single-mode optical cavity is investigated. It is found that if the cavity field is initially prepared in a thermal state and the mesoscopic Josephson junction in its lowest energy state, the coupling system can evolve into a two-mode Gaussian mixed state. The time-dependent characteristic function in the Wigner representation for the Gaussian state is analytically obtained and the linear entropy exchange between the cavity field and the mesoscopic Josephson junction subsystems is found. Furthermore, we investigate the influence of the temperature on the entanglement of the coupling system and find that the entanglement at a certain time exhibits the critical behavior with respect to the temperature of the cavity field.

Inverting Quantum Decoherence by Classical Feedback from the Environment

We show that for qubits and qutrits it is always possible to perfectly recover quantum coherence by performing a measurement only on the environment, whereas for dimension d >3 there are situations where recovery is impossible, even with complete access to the environment. For qubits, the minimal amount of classical information to be extracted from the environment equals the entropy exchange.

Entropy exchange and entanglement in the Jaynes-Cummings model

The Jaynes-Cummings model is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight (S. J. D. Phoenix, P. L. Knight, Annals of Physics 186, 381). of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e. where the rate of change of the two are anti-correlated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anti-correlation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix.

Thermodynamic stability of ecosystems

The stability of ecosystems during periods of stasis in their macro-evolutionary trajectory is studied from a non-equilibrium thermodynamic perspective. Individuals of the species are considered as units of entropy production and entropy exchange in an open thermodynamic system. Within the framework of the classical theory of irreversible thermodynamics, and under the condition of constant external constraints, such a system will naturally evolve toward a globally stable thermodynamic stationary state. It is thus suggested that the ecological steady state, or stasis, is a particular case of the thermodynamic stationary state, and that the evolution of community stability through natural selection is a manifestation of non-equilibrium thermodynamic directives. Furthermore, it is argued that punctuation of stasis leading to ecosystem succession, may be a manifestation of non-equilibrium “phase transitions” brought on by a change of external constraints through a thermodynamic critical point.