Finite Bath Research Articles

Study of the Adsorption of Anionic Surfactants on Carbonate Rocks: Characterizations, Experimental Design, and Parameter Implementation

Controlling or reducing the adsorption of surfactants on reservoir rock surfaces has been a challenging task in enhanced oil recovery (EOR) methods, as it directly affects the cost-effectiveness of the projects. The adsorption of surfactants on rock surfaces can modify their hydrophobicity, surface charge, and other important parameters that govern EOR processes, such as reducing the interfacial tension between water and oil and increasing permeability. Therefore, understanding the adsorption mechanism on rocks is essential for developing alternatives that improve the effectiveness of these processes. In this work, the adsorption of surfactants on carbonate materials was evaluated considering variations in temperature, contact time, and surfactant concentration. The surfactants used were derived from vegetable oils, aiming for a sustainable approach: saponified coconut oil (SCO), saponified babassu coconut oil (SBCO), and saponified castor oil (SMO). The finite bath method was used, resulting in adsorption efficiencies of 85.74%, 82.52%, and 45.30% for SCO, SBCO, and SMO, respectively. The Sips isotherm and the pseudo-second-order model were found to be suitable for characterizing these systems. The simulation of SCO adsorption isotherms on limestone by the Langmuir model was more accurate than that using the Freundlich model. The limestone showed a negative surface charge of approximately −35.0 mV at pH 6.5; this negative charge varied over a wide pH range. These zeta potential data for the samples confirmed that hydrophobic interactions played an important role in the adsorption of the surfactants. Thermodynamic evaluation indicated spontaneous and endothermic adsorption of SCO on limestone. The systems were also characterized by FTIR, TG/DTG, XRD, XRF, SEM, and zeta potential.

Boyd’s film diffusion model for water contaminant adsorption: Time for an upgrade?

The Boyd film diffusion model is widely used in liquid phase adsorption studies for its mathematical simplicity and straightforward data analysis. However, a lack of awareness regarding its restrictive assumptions has led to widespread misuse. The Boyd model assumes film diffusion as the rate-controlling mechanism and rests on two additional pivotal assumptions: adsorption occurs under infinite bath conditions and follows a linear equilibrium relationship. This study examines the recurrent breaches of these assumptions across a growing body of research on water contaminant adsorption. Nearly all kinetic data have been derived from finite bath experiments governed by nonlinear isotherms, which directly contradict the Boyd model’s assumptions. Consequently, applying the Boyd model to such data can yield misleading results and interpretations. To address these challenges, alternative models tailored for finite bath conditions and capable of accommodating both linear and nonlinear isotherms should be considered. These models offer more accurate insights into adsorption kinetics under realistic experimental settings. While the Boyd model remains valuable under specific conditions, its stringent assumptions restrict its broader applicability. Researchers should critically assess the validity of these assumptions and explore alternative models when analyzing liquid phase adsorption kinetics to ensure robust and reliable results.

Page curve of AdS-Vaidya model for evaporating black holes

We study an evaporating black hole in the boundary conformal field theory (BCFT) model under the fully time-dependent AdS-Vaidya spacetime geometry. We introduce the time-dependent finite bath termed the effective Hawking radiation region. This is described by a nontrivial BCFT solution that acts as a time-dependent brane which we call the moving end-of-the-radiation (METR) brane that leads to a new type of Hubeny-Rangamani-Takayanagi surface. We further examine the island formulation in this particular time-dependent spacetime. The Page curve is calculated by using Holographic Entanglement Entropy (HEE) in the context of double holography.

Modeling the dynamics of quantum systems coupled to large-dimensional baths using effective energy states.

The quantum dynamics of a low-dimensional system in contact with a large but finite harmonic bath is theoretically investigated by coarse-graining the bath into a reduced set of effective energy states. In this model, the couplings between the system and the bath are obtained from statistically averaging over the discrete, degenerate effective states. Our model is aimed at intermediate bath sizes in which non-Markovian processes and energy transfer between the bath and the main system are important. The method is applied to a model system of a Morse oscillator coupled to 40 harmonic modes. The results are found to be in excellent agreement with the direct quantum dynamics simulations presented in the work of Bouakline et al. [J. Phys. Chem. A 116, 11118-11127 (2012)], but at a much lower computational cost. Extension to larger baths is discussed in comparison to the time-convolutionless method. We also extend this study to the case of a microcanonical bath with finite initial internal energies. The computational efficiency and convergence properties of the effective bath states model with respect to relevant parameters are also discussed.

Imidazolate framework material for crude oil removal in aqueus media: Mechanism insight

Considerable amount of produced water discharged by the oil industry contributes to an environmental imbalance due to the presence of several components potentially harmful to the ecosystem. We investigated the factors influencing the adsorption capacity of Zinc Imidazolate Framework-8 (ZIF-8) in finite bath systems for crude oil removal from petroleum extraction in synthetic produced water. ZIF-8, experimentally obtained by solvothermal method, was characterized by XRD, FTIR, TGA, BET and its point of zero charge (pHpcz) was determined. Synthesized material showed high crystallinity, with surface area equal to 1558 m2 g−1 and thermal stability equivalent to 400 °C. Adsorption tests revealed, based on the Sips model, that the process takes place in a heterogeneous system. Additionally, intraparticle diffusion model exhibited multilinearity characteristics during adsorption process. Thermodynamic investigation demonstrated that adsorption process is spontaneous and exothermic, indicating a physisorption phenomenon. These properties enable the use of ZIF-8 in oil adsorption, which presented an adsorption capacity equal to 452.9 mg g−1. Adsorption mechanism was based on hydrophobic interactions, through apolar groups present on ZIF-8 structure and oil hydrocarbons, and electrostatic interactions, through the difference in charges between positive surface of adsorbent and negatively charged oil droplets.

Theory dependence of black hole interior reconstruction and the extended strong subadditivity

An AdS eternal black hole in equilibrium with a finite temperature bath presents a Hawking-like information paradox due to a continuous exchange of radiation with the bath. The non-perturbative gravitational effect, the replica wormhole, cures this paradox by introducing a non-trivial entanglement wedge for the bath after Page time. In this paper, we analyse the theory dependence of this non-perturbative effect by randomising the boundary conditions of some of the bulk matter fields. We explicitly analyse this in JT gravity by introducing a matter CFT in the AdS region with random boundary conditions at the AdS boundary that are drawn from a distribution. Using the island formula and the extended strong subadditivity due to Carlen and Lieb, we show that at late times the black hole interior is contained inside the entanglement wedge of a reference Hilbert space that encodes the information about the random boundary conditions. Consequently, the reconstruction of the black hole interior from the radiation, in particular the region near the singularity, requires a detailed knowledge of the theory.

PERFORMANCE OF AMAZONIAN BIOSORBENTS IN THE SEPARATION PROCESS OF EMULSIFIED OIL WITH RIO NEGRO WATER

Currently, one of the most serious environmental problems society is facing is water contamination by oil spills. The use of sorbents from agricultural residues has been considered a very promising approach for the effective treatment of oil contaminated water. Therefore, this work investigates the use of biosorbents obtained from cupuaçu shell (Bio-CP) and sacha inchi shell (Bio-SI) in the oil removal process. The characterization of adsorbents was carried out by FTIR, XRF, and TGA. Adsorption tests were carried out in a finite bath using 0.1 g of biosorbent and diesel/Rio Negro water emulsions at 400 mg.L-1 in a contact time of 60 minutes. The results show that Bio-CP has a higher oil adsorption capacity (190.8 mg.g-1) compared to Bio-SI (174.93 mg.g-1), and better oil removal, 95.4%, if compared to 87.47% for Bio-SI. The results indicate that cupuaçu and sacha inchi shells can be effective in the production of biosorbents to remove diesel from contaminated water.

Exact entanglement dynamics of two spins in finite baths

Exact entanglement dynamics of two spins in finite baths

Long-Time Relaxation of a Finite Spin Bath Linearly Coupled to a Qubit

We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of [Formula: see text] spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime [Formula: see text], assuming that the qubit–bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behaviour is captured by an analytical approximation that makes use of the property [Formula: see text] to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.

Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach

Understanding the thermodynamics of driven quantum systems strongly coupled to thermal baths is a central focus of quantum thermodynamics and mesoscopic physics. A variety of different methodological approaches exist in the literature, all with their own advantages and disadvantages. The mesoscopic leads approach was recently generalised to steady state thermal machines and has the ability to replicate Landauer B\"uttiker theory in the non-interacting limit. In this approach a set of discretised lead modes, each locally damped, provide a markovian embedding for the baths. In this work we further generalise this approach to incorporate an arbitrary time dependence in the system Hamiltonian. Following a careful discussion of the calculation of thermodynamic quantities we illustrate the power of our approach by studying several driven mesoscopic examples coupled to finite temperature fermionic baths, replicating known results in various limits. In the case of a driven non interacting quantum dot we show how fast driving can be used to induce heat rectification.

Frustration shapes multi-channel Kondo physics: a star graph perspective

We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalisation group technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids (NFLs). The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature. Despite the absence of inter-channel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them. A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local NFLs arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signalling the underlying orthogonality catastrophe associated with the degenerate ground state manifold. We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling.

Emergence of steady currents due to strong prethermalization

A steady current between baths is a manifestation of the prethermalization phenomenon, a quasi-equilibrium dynamical process with weak conserved quantity breaking. We consider two finite nonintegrable many-body baths each following the eigenstate thermalization hypothesis, and each prepared in a random product state with fixed and different energy constraints, i.e., within the mean energy ensemble. Such an initialization, not being constrained to superpositions or mixtures of many-body eigenstates, opens the door to experimental realization and also significantly simplifies numerical simulations. We show that such dynamical process is typical as the current variance decreases exponentially with respect to the size of baths. We also demonstrate that the emerging current is prethermalized in a strong sense, analogously to strong thermalization, meaning that the current values stay close to the microcanonical one for most of the time.

Collapse and revival structure of information backflow for a central spin coupled to a finite spin bath

The Markovianity of quantum dynamics is an important property of open quantum systems determined by various ingredients of the system and bath. Apart from the system-bath interaction, the initial state of the bath, etc., the dimension of the bath plays a critical role in determining the Markovianity of quantum dynamics, as a strict decay of the bath correlations requires an infinite dimension for the bath. In this work, we investigate the role of finite bath dimension in the Markovianity of quantum dynamics by considering a simple but nontrivial model in which a central spin is isotropically coupled to a finite number of bath spins, and show how the dynamics of the central spin transits from non-Markovian to Markovian as the number of the bath spins increases. The non-Markovianity is characterized by the information backflow from the bath to the system in terms of the trace distance of the system states. We derive the time evolution of the trace distance analytically, and find periodic collapse-revival patterns in the information flow. The mechanism underlying this phenomenon is investigated in detail, and it shows that the period of the collapse-revival pattern is determined by the competition between the number of the bath spins, the system-bath coupling strength, and the frequency detuning. When the number of bath spins is sufficiently large, the period of the collapse-revival structure as well as the respective collapse and revival times increase in proportion to the number of the bath spins, which characterizes how the information backflow decays with a large dimension of the bath. We also analyze the effect of the system-bath interaction strength and frequency detuning on the collapse-revival patterns of the information flow, and obtain the condition for the existence of the collapse-revival structure. The results are illustrated by numerical computation.

Strongly coupled quantum Otto cycle with single qubit bath.

We discuss a model of a closed quantum evolution of two qubits where the joint Hamiltonian is so chosen such that one of the qubits acts as a bath and thermalizes the other qubit which is acting as the system. The corresponding exact master equationfor the system is derived. Interestingly, for a specific choice of parameters the master equationtakes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form, with constant coefficients representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite baths, including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for the heat engine regime (refrigerator regime), and for different modifications of the joint Hamiltonian.

Simulating spin measurement with a finite heat bath model for the environment

Spin measurement is studied as a unitary time evolution of the spin coupled to an environment representing the meter and the apparatus. Modelling the environment as a heat bath comprising only a finite number of boson modes and represented in a basis of coherent states, following the Davydov ansatz, it can be fully included in the quantum time evolution of the total system. We perform numerical simulations of projective measurements of the polarization, with the spins prepared initially in a neutral pure state. The likewise pure initial state of the environment is constructed as a product of coherent states of the boson modes with a random distribution of their centroids around the origin of phase space. Switching the self-energy of the spin and the coupling to the heat bath on and off by a time-dependent modulation, we observe the outcome of the measurement in terms of the long-time behaviour of the spin. Interacting with the heat bath, the spins get entangled with it and lose coherence, thus reproduce the "collapse of the wavefunction". The expected quantum randomness in the final state is manifest in our simulations as a tendency of the spin to approach either one of the two eigenstates of the measured spin operator, recovering an almost pure state. The unitary time evolution allows us to reproducibly relate these random final states to the respective initial states of the environment and to monitor the exchange of information between the two subsystems in terms of their purity and mutual entropy.

Quantum Energy Current Induced Coherence in a Spin Chain under Non-Markovian Environments

We investigate the time-dependent behaviour of the energy current between a quantum spin chain and its surrounding non-Markovian and finite temperature baths, together with its relationship to the coherence dynamics of the system. To be specific, both the system and the baths are assumed to be initially in thermal equilibrium at temperature and , respectively. This model plays a fundamental role in study of quantum system evolution towards thermal equilibrium in an open system. The non-Markovian quantum state diffusion (NMQSD) equation approach is used to calculate the dynamics of the spin chain. The effects of non-Markovianity, temperature difference and system-bath interaction strength on the energy current and the corresponding coherence in cold and warm baths are analyzed, respectively. We show that the strong non-Markovianity, weak system-bath interaction and low temperature difference will help to maintain the system coherence and correspond to a weaker energy current. Interestingly, the warm baths destroy the coherence while the cold baths help to build coherence. Furthermore, the effects of the Dzyaloshinskii–Moriya () interaction and the external magnetic field on the energy current and coherence are analyzed. Both energy current and coherence will change due to the increase of the system energy induced by the interaction and magnetic field. Significantly, the minimal coherence corresponds to the critical magnetic field which causes the first order phase transition.

Open quantum systems coupled to finite baths: A hierarchy of master equations.

An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium but it induces a dynamical evolution of the bath state. In this paper, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equationsthat improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy, we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which not only is more realistic but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular noninteracting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equationsto study the central spin model.

Theory of two-component irreversible adsorption with pore diffusion control

• Theory of pore-diffusion controlled multi-component irreversible adsorption. • Shrinking core model for multi-component irreversible binding. • Closed-form expressions for batch uptake and column breakthrough. • Solutions validated by numerical simulation with the general rate model. This paper provides a theoretical analysis of the kinetics of two-component irreversible adsorption in porous spherical particles for conditions where pore diffusion is limiting. The two components are assumed to have the same binding capacity without the possibility of displacement of one component by the other but with different effective pore diffusivities. As a result, the amounts of each component adsorbed depend on the relative rates of mass transfer within the particles. Closed-form analytical expressions derived by solving the relevant conservation equations are obtained to describe adsorption from an infinite bath with constant concentrations at the particle surface, batch adsorption in a finite bath, and adsorption in packed columns, both under constant pattern and non-constant pattern conditions. In each case, the expression derived reduces to a single integral. These expressions are in good agreement with the numerical solutions of the corresponding general rate model for conditions where the kinetics of binding is fast and provide a simple means to predict two-component adsorption in many practical cases where strong adsorption conditions prevail. Generalizations to systems with more than two components, to cases where the external mass transfer resistance is important, and to unequal capacities are also provided.

Partial thermalisation of a two-state system coupled to a finite quantum bath

The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially thermalising system composed of a spin-\tfrac{1}{2}12 coupled to a finite quantum bath. The spin-bath coupling is sufficiently weak that ETH does not apply, but sufficiently strong that perturbation theory fails. We calculate (i) the distribution of fidelity susceptibilities, which takes a broadly distributed form, (ii) the distribution of spin eigenstate entropies, which takes a bi-modal form, (iii) infinite time memory of spin observables, (iv) the distribution of matrix elements of local operators on the bath, which is non-Gaussian, and (v) the intermediate entropic enhancement of the bath, which interpolates smoothly between S = 0S=0 and the ETH value of S = \log 2S=log2. The enhancement is a consequence of rare many-body resonances, and is asymptotically larger than the typical eigenstate entanglement entropy. We verify these results numerically and discuss their connections to the many-body localisation transition.

Maximum entropy and constraints in composite systems.

The principle of maximum entropy (PME), as expounded by Jaynes, is based on the maximization of the Boltzmann-Gibbs-Shannon (BGS) entropy subject to linear constraints. The resulting probability distributions are of canonical (exponential) form. However, the rationale for linear constraints is nebulous, and probability distributions are not always canonical. Here we show that the correct noncanonical distribution for a system in equilibrium with a finite heat bath is implied by the unconstrained maximization of the total BGS entropy of the system and bath together. This procedure is shown to be equivalent to maximizing the BGS entropy of the system alone subject to a contrived nonlinear constraint which reduces to (a) the usual linear constraint for an infinite heat bath, and (b) a previously enigmatic logarithmic constraint which implies a power-law distribution for a large but finite heat bath. This procedure eliminates the uncertainty as to the proper constraints, and easily generalizes to arbitrary composite systems, for which it provides a simpler alternative to the Jaynes PME.