Entropy Exchange Research Articles

Living organisms from Prigogine’s perspective: an opportunity to introduce students to biological entropy balance

All living structures, from archaea to human, are open thermodynamic systems analysed through nonequilibrium thermodynamics. Nonequilibrium thermodynamics is a field with important applications to life sciences, which is very often left out of life science courses. A three-step method is suggested to make an easy introduction of nonequilibrium thermodynamics to life science students. The first step is to introduce the Prigogine equation dS = deS + diS, and explain the meaning of the entropy exchange with the surroundings deS and internal entropy generation in the system diS. The second step is to show that the Prigogine equation is connected to the equilibrium thermodynamics already known to students. This can be done by deriving the Clausius inequality dS ≥ dq/T, from the Prigogine equation applied to reversible and irreversible processes in closed systems. Reversible and irreversible processes are discussed separately and the results are then combined into the Clausius inequality. The third step is to introduce the fact that the Prigogine equation has a variety of applications in life sciences. This would give the students an opportunity to understand the entropy balance of physiological processes in cells and organisms. The import and accumulation of entropy, entropy generation, and entropy export could be made easier for students to adopt.

Entropy model of dissipative structure on corporate social responsibility

Enterprise is prompted to fulfill the social responsibility requirement by the internal and external environment. In this complex system, some studies suggest that firms have an orderly or chaotic entropy exchange behavior. Based on the theory of dissipative structure, this paper constructs the entropy index system of corporate social responsibility(CSR) and explores the dissipative structure of CSR through Brusselator model criterion. Picking up listed companies of the equipment manufacturing, the research shows that CSR has positive incentive to negative entropy and promotes the stability of dissipative structure. In short, the dissipative structure of CSR has a positive impact on the interests of stakeholders and corporate social images.

Self‐Assembly of Poly(vinylpyridine‐b‐oligo(ethylene glycol) methyl ether methacrylate) Diblock Copolymers

ABSTRACTPoly(oligoethylene glycol)‐poly(2‐vinylpyridine) is a model diblock for studying the effect of block‐localized charge on block copolymer self‐assembly because in the absence of charge the polymers are perfectly miscible, and upon protonation of the vinylpyridine block the polymer undergoes an order–disorder transition. Seven model block copolymers with molecular weights of approximately 60 kDa containing poly(2‐vinylpyridine) volume fractions spanning 0.069–0.700 were synthesized using reversible addition fragmentation transfer polymerization and then studied to understand the effect of protonation level, diblock composition, and temperature on the location of the ordering transition and the type of nanostructures formed in a charge asymmetric system. All of the polymers displayed lower critical solution‐type behavior, with the order–disorder transition temperature decreasing with increasing acid content. Polymers with symmetric compositions showed the highest degree of incompatibility for a given degree of protonation, and the observed morphologies for all polymers were consistent with those observed at similar compositions for classical hydrophobic block copolymers. The observed protonation‐induced phase transition can be explained by the shift of the Flory–Huggins parameter due to the alternation of the identity of monomers, consistent with the prediction of Nakamura and Wang's theory. The use of polyvalent ions promotes self‐assembly at lower concentrations, consistent with ionic crosslinking effects between polymer chains that are promoted at high concentration due to exchange entropy in crosslinked polymers. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 1181–1190

MINIMUM OF EXERGY LOSSES IN NON-EQUILIBRIUN PROCESSE OF ACTUATING MEDIUMS HEAT EXCHANGE

In course of calculation of heat-exchange equipment, major parameters at which heat-exchanging process between heat-carriers runs with possible lesser losses of operational part of heat are defined by methods of thermo-dynamic. In comparison to developed methods of equilibrium processes of actuating mediums heat-exchange calculation, non-equilibrium is at stage of improvement. The research, allowing the defining minimum of entropy production and, accordingly, minimum of exergy losses in non-equilibrium processes of actuating media heat-exchange, is performed. Results of researches are valid both to externally non-equilibrium processes and polytropic. There is defined a dependency of the thermodynamic system entropy growth from the relation of the upper and lower boundary temperatures, independently from the operating media flow process in the heat-exchangers. There is shown that in certain degree of irreversibility the numerical value of which is determined technologically and structurally, there are the relations of thermodynamic parameters for which the operation media heat exchange entropy growth reaches of the minimum numerical value. As confirmation of analysis results example is presented, in which, on several variants, is shown course of entropy production of thermo-dynamic system through minimum that corresponds to the performed research. The carried analysis can find its application both in engineering works and analytical investigations. Bibl. 8, Fig. 1, Tab. 1.

Entropy exchange for infinite-dimensional systems

In this paper the entropy exchange for channels and states in infinite-dimensional systems are defined and studied. It is shown that, this entropy exchange depends only on the given channel and the state. An explicit expression of the entropy exchange in terms of the state and the channel is proposed. The generalized Klein’s inequality, the subadditivity and the triangle inequality about the entropy including infinite entropy for the infinite-dimensional systems are established, and then, applied to compare the entropy exchange with the entropy change.

CoMg olivine: cation partitioning, thermal expansion and structural variation studied by in situ neutron and synchrotron powder diffraction

The crystal structure of CoMg olivine has been investigated by in situ neutron and synchrotron X-ray powder diffraction at temperatures between 23°C and 1050°C. The olivine sample was prepared at 1450°C by solid-state reaction. During quench, the structure acquired a partially anti-ordered Co,Mg site occupancy, X Co M 1 > X Co M 2 , which upon ensuing heating persisted up to 550°C due to slow exchange kinetics. Above 600°C, internal equilibrium was readily obtained. The temperature variation of the Co,Mg site occupancies was modelled by R T ln( K D )= − 12080 ( ±620 ) −160 ( ±0.58 ) T [ J mol − 1 ]. The pronounced negative exchange enthalpy strongly favours the anti-ordered state, as does the positive exchange entropy so that CoMg olivine will remain in this state up to the melting point. The anisotropy of thermal expansion was analysed using an isothermal equation-of-state (EoS) (Kumar, 1995) coupled with the thermal Mie-Gruneisen EoS. This coupling allowed for relating the anisotropic expansivity to an anisotropic thermal pressure. Both properties are linked to the temperature-dependent rotations of the M1 and M2 octahedra in the [001] plane. The rotations increase from Mg via CoMg to Fe olivine. The Kumar and Birch-Murnaghan EoS’s gave virtually indistinguishable results upon modelling thermal expansion. The increase of the mean bond distances and with temperature changes at ~550°C when the redistribution of Co and Mg begins. In terms of a distortion parameter defined as a normalized standard deviation, the bond length distortion of the M2 octahedron is larger than that of M1. Conversely, M1 is more distorted than M2, if the distortion is defined by the variation of the octahedral faces as well as by the variation of the O-M-O angles subtended at the M sites. The former distortion relates to the exchange entropy.

Quantum Coarse-Graining: An Information-theoretic Approach to thermodynamics

We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on this gap. We then introduce a fully information-theoretic framework generalizing the above by making further abstraction of physical quantities such as energy. It is technically convenient to work with and reproduces known results for finite-size quantum thermodynamics. With our framework we may determine the minimal work cost of implementing any logical process. In the case of information processing on memory registers with a degenerate Hamiltonian, the answer is given by the max-entropy, a measure of information known from quantum information theory. In the general case, we obtain a new information measure, the coherent relative entropy, which generalizes both the conditional entropy and the relative entropy. It satisfies a collection of properties which justifies its interpretation as an entropy measure and which connects it to known quantities. We then present how, from our framework, macroscopic thermodynamics emerges by typicality, after singling out an appropriate class of thermodynamic states possessing some suitable reversibility property. A natural thermodynamic potential emerges, dictating possible state transformations, and whose differential describes the physics of the system. The textbook thermodynamics of a gas is recovered as well as the form of the second law relating thermodynamic entropy and heat exchange. Finally, noting that quantum states are relative to the observer, we see that the procedure above gives rise to a natural form of coarse-graining in quantum mechanics: Each observer can consistently apply the formalism of quantum information according to their own fundamental unit of information.

Multiatom Quantum Coherences in Micromasers as Fuel for Thermal and Nonthermal Machines

In this paper, we address the question: To what extent is the quantum state preparation of multiatom clusters (before they are injected into the microwave cavity) instrumental for determining not only the kind of machine we may operate, but also the quantitative bounds of its performance? Figuratively speaking, if the multiatom cluster is the “crude oil”, the question is: Which preparation of the cluster is the refining process that can deliver a “gasoline” with a “specific octane”? We classify coherences or quantum correlations among the atoms according to their ability to serve as: (i) fuel for nonthermal machines corresponding to atomic states whose coherences displace or squeeze the cavity field, as well as cause its heating; and (ii) fuel that is purely “combustible”, i.e., corresponds to atomic states that only allow for heat and entropy exchange with the field and can energize a proper heat engine. We identify highly promising multiatom states for each kind of fuel and propose viable experimental schemes for their implementation.

Nonequilibrium thermodynamic formalism of nonlinear chemical reaction systems with Waage–Guldberg’s law of mass action

Macroscopic entropy production rate σ(tot) in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation rate and a house-keeping heat dissipation rate: σ(tot)=σ(fd)+σ(hk); σ(fd)=-dA/dt, where A is a generalized free energy function. This yields a novel nonequilibrium free energy balance equation dA/dt=-σ(tot)+σ(hk), which is on a par with celebrated entropy balance equation dS/dt=σ(tot)+η(ex) where η(ex) is the rate of entropy exchange with the environment. For kinetic systems with complex balance, σ(fd) and σ(hk) are the macroscopic limits of stochastic free energy dissipation rate and house-keeping heat dissipation rate, which are both nonnegative, in the Delbrück–Gillespie description of the stochastic chemical kinetics. A full kinetic and thermodynamic theory of chemical reaction systems that transcends mesoscopic and macroscopic levels emerges.

Thermodynamic characteristics of sorption extraction and chromatographic separation of anionic complexes of erbium and cerium with Trilon B on weakly basic anionite

The adsorption of anionic complexes of erbium with Trilon B on D-403 anionite is studied at ionic strengths of 1 and 2 mol/kg (NaNO3) and temperatures of 298 and 343 K. The values of the stability constants of complex ions of REE with Trilon B and the Gibbs energies of complexation are calculated. The values of the Gibbs energy and the enthalpy and entropy of ion exchange are determined. Using the obtained thermo-dynamic and sorption characteristics, the possible separation of anionic complexes of erbium and cerium with Trilon B is demonstrated via frontal ion-exchange chromatography. A series of sorption capacities of anionic complexes of cerium, yttrium, and erbium is presented using the values of the Gibbs energy of ion exchange.

Cooling and Autonomous Feedback in a Bose-Hubbard Chain with Attractive Interactions.

We engineer a quantum bath that enables entropy and energy exchange with a one-dimensional Bose-Hubbard lattice with attractive on-site interactions. We implement this in an array of three superconducting transmon qubits coupled to a single cavity mode; the transmons represent lattice sites and their excitation quanta embody bosonic particles. Our cooling protocol preserves the particle number-realizing a canonical ensemble-and also affords the efficient preparation of dark states which, due to symmetry, cannot be prepared via coherent drives on the cavity. Furthermore, by applying continuous microwave radiation, we also realize autonomous feedback to indefinitely stabilize particular eigenstates of the array.

Thermodynamical journey in plant biology.

Nonequilibrium irreversible thermodynamics constitute a meaningful point of view suitable to explore life with a rich paradigm. This analytical framework can be used to span the gap from molecular processes to plant function and shows great promise to create a holistic description of life. Since living organisms dissipate energy, exchange entropy and matter with their environment, they can be assimilated to dissipative structures. This concept inherited from nonequilibrium thermodynamics has four properties which defines a scale independent framework suitable to provide a simpler and more comprehensive view of the highly complex plant biology. According to this approach, a biological function is modeled as a cascade of dissipative structures. Each dissipative structure, corresponds to a biological process, which is initiated by the amplification of a fluctuation. Evolution of the process leads to the breakage of the system symmetry and to the export of entropy. Exporting entropy to the surrounding environment corresponds to collecting information about it. Biological actors which break the symmetry of the system and which store information are by consequence, key actors on which experiments and data analysis focus most. This paper aims at illustrating properties of dissipative structure through familiar examples and thus initiating the dialogue between nonequilibrium thermodynamics and plant biology.

Local detailed balance: a microscopic derivation

Thermal contact is the archetype of non-equilibrium processes driven by constant non-equilibrium constraints when the latter are enforced by reservoirs exchanging conserved microscopic quantities. At a mesoscopic scale only the energies of the macroscopic bodies are accessible together with the configurations of the contact system. We consider a class of models where the contact system, as well as macroscopic bodies, have a finite number of possible configurations. The global system, with only discrete degrees of freedom, has no microscopic Hamiltonian dynamics, but it is shown that, if the microscopic dynamics is assumed to be deterministic and ergodic and to conserve energy according to some specific pattern, and if the mesoscopic evolution of the global system is approximated by a Markov process as closely as possible, then the mesoscopic transition rates obey three constraints. In the limit where macroscopic bodies can be considered as reservoirs at thermodynamic equilibrium (but with different intensive parameters), the mesoscopic transition rates turn into transition rates for the contact system and the third constraint becomes local detailed balance; the latter is generically expressed in terms of the microscopic exchange entropy variation, namely the opposite of the variation of the thermodynamic entropy of the reservoir involved in a given microscopic jump of the contact system configuration. For a finite-time evolution after contact has been switched on, we derive a fluctuation relation for the joint probability of the heat amounts received from the various reservoirs. The generalization to systems exchanging energy, volume and matter with several reservoirs, with a possible conservative external force acting on the contact system, is given explicitly.

Causal conditioning and instantaneous coupling in causality graphs

This study aims at providing the definitive links between Massey and Kramer’s directed information theory and Granger causality graphs, recently formalized by Eichler. This naturally leads to consider two concepts of causality that can occur in physical systems: dynamical causality and instantaneous coupling. Although it is well accepted that the former is assessed by conditional transfer entropy, the latter is often overlooked, even if it was clearly introduced and understood in seminal studies. In the bivariate case, we show that directed information is decomposed into the sum of transfer entropy and instantaneous information exchange. In the multivariate case, encountered for conditional graph modeling, such a decomposition does not hold anymore. We provide a new insight into the problem of instantaneous coupling and show how it affects the estimated structure of a graphical model that should provide a sparse representation of a complex system. This result is discussed and analyzed for the inference of causality graphs. Two synthetic examples are developed to illustrate the theoretical concepts. Practical issues are also briefly discussed on these examples and an extension of Leonenko’s k-nearest neighbors based entropy estimators is used to derive a nonparametric estimator of directed information.

Influence of Si substitution on the structure, magnetism, exchange bias and negative magnetoresistance in Ni48Mn39Sn13 Heusler alloys

The effect of partial Si substitution for Sn on the structure, magnetism, magnetic entropy change, exchange bias and negative magnetoresistance in Ni48Mn39Sn13−xSix(1 ⩽ x ⩽ 4) Heusler alloy systems is investigated. A small amount of Si in the Sn position influences the characteristic transition temperatures and the magnetocaloric effect. A maximum positive entropy change of 5.13 J kg−1 K−1 is observed for a field change of 9 T in the x = 1 alloy. An increase in Si content increases the exchange bias field. The exchange bias field and the coercive field strongly depend on the Si content. For the x = 4 alloy, an exchange bias field of 354 Oe is observed. In addition, a negative magnetoresistance is observed in this alloy system, which decreases with Si content. The increase in resistivity at the martensitic transition could be attributed to the formation of superzone boundary gaps that changes the density of states near the Fermi surface.

Notes on entropic characteristics of quantum channels

AbstractOne of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss a few channel characteristics expressed by means of generalized entropies. Such characteristics can often be treated in line with more usual treatment based on the von Neumann entropies. For any channel, we show that the q-average output entropy of degree q ≥ 1 is bounded from above by the q-entropy of the input density matrix. The concavity properties of the (q, s)-entropy exchange are considered. Fano type quantum bounds on the (q, s)-entropy exchange are derived. We also give upper bounds on the map (q, s)-entropies in terms of the output entropy, corresponding to the completely mixed input.

频率变化的热光场对混态J-C模型中熵交换的调控

频率变化的热光场对混态J-C模型中熵交换的调控

Vanishing quantum discord and complete entropy exchange between subsystems in a bipartite system

Vanishing quantum discord and the entropy correlations between subsystems in a bipartite system are investigated. We numerically verify that there exists a condition of complete entropy exchange between the two subsystems, and it is found that the condition is in excellent agreement with that of the nullity of quantum discord in a certain range of parameters of the bipartite system.

PTR-MS measurement of partition coefficients of reduced volatile sulfur compounds in liquids from biotrickling filters

Biological air filtration for reduction of emissions of volatile sulfur compounds (e.g., hydrogen sulfide, methanethiol and dimethyl sulfide) from livestock production facilities is challenged by poor partitioning of these compounds into the aqueous biofilm or filter trickling water. In this study, Henry’s law constants of reduced volatile sulfur compounds were measured for deionized water, biotrickling filter liquids (from the first and second stages of a two-stage biotrickling filter), and NaCl solutions by a dynamic method using Proton-Transfer-Reaction Mass Spectrometry (PTR-MS) at a temperature range of 3–45°C. NaCl solutions were used to estimate salting-out constants up to an ionic strength of 0.7M in order to evaluate the effect of ionic strength on partitioning between air and biofilter liquids. Thermodynamic parameters (enthalpy and entropy of phase exchange) were obtained from the measured partition coefficients as a function of temperature. The results show that the partition coefficients of organic sulfur compounds in the biotrickling filter liquids were generally very close to the corresponding partition coefficients in deionized water. Based on the estimated ionic strength of biofilter liquids, it is assessed that salting-out effects are of no importance for these compounds. For H2S, a higher enthalpy of air–liquid partitioning was observed for 2nd stage filter liquid, but not for 1st stage filter liquid. In general, the results show that co-solute effects for sulfur compounds can be neglected in numerical biofilter models and that the uptake of volatile sulfur compounds in biotrickling filter liquids cannot be increased by decreasing ionic strength.

Energy degradation and ecosystem development: Theoretical framing, indicators definition and application to a test case study

During the last few decades, the so-called “maximum dissipation principle” has raised a wide debate as a paradigm governing the development of ecological systems. In the present contribution, after having discussed the meaning of the term energy degradation within the framework provided by the entropy and the exergy balance, it is suggested to distinguish three different facets of the phenomenon of the energy degradation, respectively dealing with the overall, system and environmental degradation. In relation with ecological indication, the above classification shows that different types of indicators of energy degradation can be defined, thus emphasising that a clear reference to the specific facet considered should be made in order to avoid ambiguous statements. The behaviour of several thermodynamic indicators, which include previously derived indices and a new set of entropy-based indicators, is examined along the seasonal progression in a lake ecosystem, and the effectiveness of the considered indicators in characterising the development state is evaluated by comparing their responses with the main successional traits of the phytoplankton community. The results show that, although overall degradation and related indices may deserve consideration as indicators of the extent of the degradative (biotic and abiotic) processes acting within an ecosystem, their significance as indicators of development state appears to be limited. On the other hand, indicators related to environmental degradation appear to be more promising as indicators of the development state, provided that some methodological issues dealing with the effect of the abiotic noise are properly addressed. The net radiative entropy exchange shows a significant correlation with phytoplankton successional traits, thus suggesting that the entropy changes in the radiative portion of the entropy budget are the most informative in relation to the development state of aquatic communities. The methodology adopted also lends itself to be used for evaluating the energy quality associated with an energy flow, which is here measured by the energy-to-entropy ratio.