Thermodynamic Relations Research Articles

The Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method.

Quantum thermal engines have received much attention in recent years due to their potential applications. For a candidate group, harmonically trapped gases under Bose-Einstein condensation (BEC), we see little investigation on the energy transference around that transition. Therefore, we present an empirical study with rubidium-87 gas samples in a magnetic harmonic trap. We developed an empirical equation of state model to fit to our experimental dataset, expressing the pressure parameter in terms of temperature, and six technical coefficients, functions of the volume parameter and the number of atoms. By using standard thermodynamic relations, we determine the system's entropy, shown to be constant at the BEC transition, as expected. Being isentropic makes the BEC transition an energy source for non-mechanical work. Hence, we observed that the enthalpy at the BEC transition, at fixed values of the volume parameter, grows fairly linearly with the number of atoms. We fitted a linear function to that data, finding the specific enthalpy of the BEC transformation and the intrinsic enthalpic loss for BEC. We deem this study to be a step closer to practical quantum-based engines.

Generalized Quantum Fluctuation Theorem for Energy Exchange.

The nonequilibrium fluctuation relation is a cornerstone of quantum thermodynamics. It is widely believed that the system-bath heat exchange obeys the famous Jarzynski-Wójcik fluctuation theorem. However, this theorem is established in the Born-Markovian approximation under the weak-coupling condition. Via studying the energy exchange between a harmonic oscillator and its coupled bath in the non-Markovian dynamics, we establish a generalized quantum fluctuation theorem for energy exchange being valid for arbitrary coupling strength. The Jarzynski-Wójcik fluctuation theorem is recovered in the weak-coupling limit. We also find the average energy exchange exhibits rich nonequilibrium characteristics when different numbers of system-bath bound states are formed, which suggests a useful way to control the quantum heat. Deepening our understanding of the fluctuation relation in quantum thermodynamics, our result lays the foundation to design high-efficiency quantum heat engines.

COSMOPharm: Drug-Polymer Compatibility of Pharmaceutical Amorphous Solid Dispersions from COSMO-SAC.

The quantum mechanics-aided COSMO-SAC activity coefficient model is applied and systematically examined for predicting the thermodynamic compatibility of drugs and polymers. The drug-polymer compatibility is a key aspect in the rational selection of optimal polymeric carriers for pharmaceutical amorphous solid dispersions (ASD) that enhance drug bioavailability. The drug-polymer compatibility is evaluated in terms of both solubility and miscibility, calculated using standard thermodynamic equilibrium relations based on the activity coefficients predicted by COSMO-SAC. As inherent to COSMO-SAC, our approach relies only on quantum-mechanically derived σ-profiles of the considered molecular species and involves no parameter fitting to experimental data. All σ-profiles used were determined in this work, with those of the polymers being derived from their shorter oligomers by replicating the properties of their central monomer unit(s). Quantitatively, COSMO-SAC achieved an overall average absolute deviation of 13% in weight fraction drug solubility predictions compared to experimental data. Qualitatively, COSMO-SAC correctly categorized different polymer types in terms of their compatibility with drugs and provided meaningful estimations of the amorphous-amorphous phase separation. Furthermore, we analyzed the sensitivity of the COSMO-SAC results for ASD to different model configurations and σ-profiles of polymers. In general, while the free volume and dispersion terms exerted a limited effect on predictions, the structures of oligomers used to produce σ-profiles of polymers appeared to be more important, especially in the case of strongly interacting polymers. Explanations for these observations are provided. COSMO-SAC proved to be an efficient method for compatibility prediction and polymer screening in ASD, particularly in terms of its performance-cost ratio, as it relies only on first-principles calculations for the considered molecular species. The open-source nature of both COSMO-SAC and the Python-based tool COSMOPharm, developed in this work for predicting the API-polymer thermodynamic compatibility, invites interested readers to explore and utilize this method for further research or assistance in the design of pharmaceutical formulations.

Thermal fluctuations for a three-beads swimmer

We discuss a microswimmer model made of three spheres actuated by an internal active time-periodic force, tied by an elastic potential, and submitted to hydrodynamic interactions with thermal noise. The dynamical approach we use, replacing the more common kinematic one, shows the instability of the original model and the need of a confining potential to prevent the evaporation of the swimmer. We investigate the effect of the main parameters of the model, such as the frequency and phase difference of the periodic active force, the stiffness of the confining potential, the length of the swimmer and the temperature and viscosity of the fluid. Our observables of interest are the averages of the swim velocity, the energy consumption rate, the diffusion coefficient, and the swimming precision, which is limited by the energy consumption through the celebrated thermodynamic uncertainty relations. An optimum for velocity and precision is found for an intermediate frequency. Reducing the potential stiffness, the viscosity, or the length is also beneficial for the swimming performance, but these parameters are limited by the consistency of the model. Analytical approximation for many of the relevant observables is obtained for small deformations of the swimmer. We also discuss the efficiency of the swimmer in terms of its maximum precision and of the hydrodynamic, or Lighthill, criterion, and how they are connected. Published by the American Physical Society 2024

Uncertainty relations in thermodynamics of irreversible processes on a mesoscopic scale

Studies of mesoscopic structures have become a leading and rapidly evolving research field ranging from physics, chemistry, and mineralogy to life sciences. The increasing miniaturization of devices with length scales of a few nanometers is leading to radical changes in the realization of new materials and in shedding light on our understanding of the fundamental laws of nature that govern the dynamics of systems at the mesoscopic scale. We investigate thermodynamic processes in small systems in Onsager’s region based on recent experimental results and previous theoretical research. We show that fundamental quantities such as the total entropy production, the thermodynamic variables conjugate to the thermodynamic forces, and the Glansdorff–Prigogine’s dissipative variable may be discretized at the mesoscopic scale. We establish the canonical com- mutation rules (CCRs) valid at the mesoscopic scale. The numerical value of the discretization constant is estimated experimentally. The ultraviolet divergence problem is solved by applying the correspondence principle with Einstein–Prigogine’s fluctuations theory in the limit of macroscopic systems. Examples of quantization of thermodynamic systems out of the Onsager region are currently being finalized.

Cotunneling Effects in the Geometric Statistics of a Nonequilibrium Spin‐Resolved Junction

AbstractIn the nonequilibrium steady state of electronic transport across a spin‐resolved quantronic junction, the role of cotunneling on the emergent statistics under phase‐different adiabatic modulation of the reservoirs' chemical potentials is investigated. By explicitly identifying the sequential and inelastic cotunneling rates, the geometric or Pancharatnam–Berry contribution to the spin exchange flux between the spin system and the right reservoir is numerically evaluated. The relevant conditions wherein the sequential and cotunneling processes compete and selectively influence the total geometric flux upshot are identified. The Fock space coherences are found to suppress the cotunneling effects when the system reservoir couplings are comparable. The cotunneling contribution to the total geometric flux can be made comparable to the sequential contribution by creating a right‐sided asymmetrically stronger system‐reservoir coupling strength. Using a recently proposed geometric thermodynamic uncertainty relationship, the total rate of minimal entropy production is estimated. The geometric flux and the minimum entropy is found to be nonlinear as a function of the interaction energy of the junctions' spin orbitals.

Microscopic state equation for oscillator chains

Systems allowing anomalous transport of mass, momentum energy, etc., such as low-dimensional particles systems or highly confining media, are hard to characterize thermodynamically. Indeed, local thermodynamic equilibrium may not be established and their behaviour often strongly depends on many microscopic parameters, including the symmetry of the interaction potentials. Thermodynamic state equations, on the other hand, involve a small set of observables, which are obtained averaging in time and over the large number of particles that populate mesoscopic cells in which local equilibrium can be realized. In this work we show that a linear relation discovered earlier, that connects the average distance between pairs of consecutive particles with their kinetic energy, applies to quite a large set of 1-dimensional particle systems known to produce anomalous transport. This relation is microscopic in nature, since the quantities involved are neither averaged over many particles, neither over very large times. Nevertheless, its robustness is under variations of the external parameters, and the limited set of quantities it involves qualify it as a state equation, analogously to thermodynamic relations. We provide conditions for which the relation can be violated within a limited range of parameters values, and we find that it can be extended to two-dimensional networks of coupled oscillators. The validity of this relation further shows that the states of aggregation of matter in low-dimensional systems are often different from standard macroscopic ones.

Local thermodynamics and entropy for relativistic hydrostatic equilibrium

By refining the method proposed in Aoki et al. (2021) [5], entropy current and entropy density for a relativistic hydrostatic equilibrium system with spherical symmetry are constructed as a non-Nöther conserved charge in the Einstein gravity with cosmological constant. It is shown that the constructed entropy density satisfies both the local Euler relation and the first law of thermodynamics non-perturbatively with respect to the Newton constant. Finally the established relativistic thermodynamics is applied to one of the systems with uniform energy density as a crude model of a degenerate star and its local thermodynamic observables are determined analytically.

Thermodynamic analysis of a heat engine: experiments with the Stirling cycle

This paper presents a practical thermodynamic analysis of a desktop Stirling engine to demonstrate some of the fundamental principles involving the conversion of heat to work as part of an introductory undergraduate course. Experimental measurements of temperature, pressure and volume using an Arduino microcontroller allows for the construction of P-ν and T-s process diagrams from thermodynamic relationships. By comparing the quantitative data from actual and ideal cycles, the Stirling engine represents an effective teaching tool for reinforcing core content with students.

Viscosity in simple fluids: A different perspective based on the thermodynamic dimension

This work presents a different perspective on viscosity and a new interpretation of it by treating the fluid as a fractal lattice incorporating temporary molecular clusters (t-clusters) and using the thermodynamic dimension (DT) idea. The DT connects fluid viscosity to its EoS by computing the effective intermolecular potential, U(r, T), which may be found via thermodynamic relations from the fluid equation of state (EoS). Finally, a general viscosity equation is developed utilizing standard and well-established statistical thermodynamic relations. The approach is applied to nitrogen fluid as a case study because of the fluid's extensiveness data in the literature. Less than 2 % is the absolute average deviation percent (AAD%) for viscosity prediction in the range of 65 K to 1000 K for pressures less than 2000 MPa. It is simple to code the viscosity equation that is obtained.

Thermodynamic uncertainty relation for quantum entropy production.

In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum observables, which we refer to as a thermodynamic uncertainty relation (TUR) for the entropy production. In the absence of coherence between the states, our result reproduces classic TURs in stochastic thermodynamics. For the derivation of the TUR, we introduce a lower bound for a quantum generalization of the χ^{2} divergence between two states and discuss its implications for stochastic and quantum thermodynamics, as well as the limiting case where it reproduces the quantum Cramér-Rao inequality.

Anomalous thermodynamic cost of clock synchronization

Clock synchronization is critically important in positioning, navigation and timing systems. While its performance has been intensively studied in a wide range of disciplines, much less is known for the fundamental thermodynamics of clock synchronization‒what limits the precision and how to optimize the energy cost for clock synchronization. Here, we report the first experimental investigation of two stochastic autonomous clocks synchronization, unveiling the thermodynamic relation between the entropy cost and clock synchronization in an open cavity optomechanical system. Two interacting clocks are synchronized spontaneously owing to the disparate decay rates of hybrid modes by engineering the controllable cavity-mediated dissipative coupling. The measured dependence of the degree of synchronization on the overall entropy cost exhibits an unexpected non-monotonic characteristic, while the relation between the degree of synchronization and the entropy cost for the synchronization is monotonically decreasing. The investigation of transient dynamics of clock synchronization exposes a trade-off between energy and time consumption. Our results demonstrate the possibility of clock synchronization in an effective linear system, reveal the fundamental relation between clock synchronization and thermodynamics, and have a great potential for precision measurements, distributed quantum networks, and biological science.

Blackbody heat capacity at constant pressure

At first glance, the title of this work seems to be improper. And the reason is well known. Since blackbody pressure depends only on temperature, one cannot take the derivative of the thermodynamic quantities with respect to one of them, keeping the other constant. That is, the heat capacity at constant pressure, C P , as well as, the coefficient of thermal expansion, α, and the isothermal compressibility, κ T , are ill-defined quantities. This work will show that when the perfect conducting nature of the walls of a blackbody cavity is taken into account, C P , α and κ T are in fact well defined, and they are related by the usual thermodynamic relations, as expected. Two geometries will be considered, namely, a spherical shell and a cubic box. It will be shown that C P , α and κ T depend very much on the geometry of the cavity. Issues regarding thermodynamic stability will be addressed, revealing that they also depend on the cavity’s geometry. It is argued that these findings may be amenable to experimental verification.

Thermodynamic cost for precision of general counting observables.

We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.

Two applications of stochastic thermodynamics to hydrodynamics

Recently, the theoretical framework of stochastic thermodynamics has been revealed to be useful for macroscopic systems. However, despite its conceptual and practical importance, the connection to hydrodynamics has yet to be explored. In this Letter, we reformulate the thermodynamics of compressible and incompressible Newtonian fluids so that it becomes comparable to stochastic thermodynamics and unveil their connections; we obtain the housekeeping–excess decomposition of the entropy production rate (EPR) for hydrodynamic systems and find a lower bound on EPR given by relative fluctuation similar to the thermodynamic uncertainty relation. These results not only prove the universality of stochastic thermodynamics but also suggest the potential extensibility of the thermodynamic theory of hydrodynamic systems. Published by the American Physical Society 2024

Remnant Copper Cation-Assisted Atom Mixing in Multicomponent Nanoparticles.

Nanostructured high-/medium-entropy compounds have emerged as important catalytic materials for energy conversion technologies, but complex thermodynamic relationships involved with the element mixing enthalpy have been a considerable roadblock to the formation of stable single-phase structures. Cation exchange reactions (CERs), in particular with copper sulfide templates, have been extensively investigated for the synthesis of multicomponent heteronanoparticles with unconventional structural features. Because copper cations within the host copper sulfide templates are stoichiometrically released with incoming foreign cations in CERs to maintain the overall charge balance, the complete absence of Cu cations in the nanocrystals after initial CERs would mean that further compositional variation would not be possible by subsequent CERs. Herin, we successfully retained a portion of Cu cations within the silver sulfide (Ag2S) and gold sulfide (Au2S) phases of Janus Cu2-xS-M2S (M = Ag, Au) nanocrystals after the CERs, by partially suppressing the transformation of the anion sublattice that inevitably occurs during the introduction of external cations. Interestingly, the subsequent CERs on Janus Cu1.81S-M2S (M = Ag, Au), by utilizing the remnant Cu cations, allowed the construction of Janus Cu1.81S-AgxAuyS, which preserved the initial heterointerface. The synthetic strategy described in this work to suppress the complete removal of the Cu cation from the template could fabricate the CER-driven heterostructures with greatly diversified compositions, which exhibit unusual optical and catalytic properties.

Nuclear reactions in gaseous stars: Perspectives from kinetic theory and thermodynamics

In the Standard Model of gaseous stars, temperature is primary both in the initiation of thermonuclear reactions to form heavier elements and the emission of radiation. These processes have been described using thermodynamic expressions. However, within any given thermodynamic relation, not only must units balance on each side, but so must thermodynamic character. Temperature, whether or not equilibrium conditions are established, must always be intensive in macroscopic thermodynamics, and mass must be extensive. This ensures that the laws of thermodynamics are respected. The theory of temperatures and nuclear reactions within gaseous stars is constructed from the kinetic theory of an ideal gas, by which temperature is introduced, in combination with gravitational and Coulomb forces. The resulting thermodynamic relations impart a nonintensive character to temperature and a nonextensive character to mass. Consequently, the theory of nuclear reactions in gaseous stars is invalid. Deprived of the only theoretical means by which the Standard Model justifies stellar nuclear reactions, the theory of gaseous stars is not viable. The most reasonable alternative rests in lattice confinement fusion and the recognition that the stars are comprised of condensed matter, namely metallic hydrogen.

Thermodynamics of Pickup Ions in the Heliosphere

The paper shows the thermodynamic nature of the evolution of the pickup ion (PUI) distributions through their incorporation and subsequent expansion as the solar wind moves outward through the heliosphere. In particular, the PUI expansive cooling is connected to thermodynamic polytropic processes and the thermodynamic kappa parameter. Previously, the characterization of the cooling was phenomenologically given by a “cooling index” α, which is the exponent involved in the power-law relationship between PUI speed and position. Here, we develop the relationship between the cooling and polytropic indices. Then, we show the connection between the cooling index and the thermodynamic parameter kappa. Finally, we verify the derived thermodynamic relations with direct heliospheric observations over varying distances from the Sun. Going forward, we suggest that studies of PUIs seeking to understand the underlying physics of these important particles rely on the thermodynamic parameter of kappa, and its association with the polytropic index, and not on an ad hoc cooling index.

Enhancing economic and performance effectiveness of a geo-solar system using multi aspect artificial neural network

Geo-solar systems, comprising ground-source heat pumps (GSHP) and solar thermal collectors, offer promising solutions for sustainable space heating and hot water provision in residential buildings. However, optimizing these systems for maximum energy efficiency and cost-effectiveness remains a challenge. In this context, this study presents a comprehensive approach to enhancing the performance and cost-effectiveness of geo-solar systems. The proposed methodology integrates artificial neural network (ANN) techniques and multi-aspect optimization to optimize system parameters. The detailed of building mathematical model incorporating energy and exergy equations, thermodynamic, and economic relations for all system components. The neural network model inputs to the include five neurons represents Geothermal temperature, Solar radiation levels, System pressure levels, Ambient temperature, and Operational time, and the model outputs represent Energy efficiency and Exergy destruction rate. Through the training of ANN using simulation data and the application of a multi-objective genetic algorithm, the system is optimized for energy efficiency, cost, and environmental impact simultaneously. The results of analysis show that the exergy efficiency of system is 22.02 % and turbine generates 1963 kW. Changes in P10, ranging from 2000 to 3400 kPa leads to the exergy destruction reduction from 8350 kW to 8000 kW, while the other parameters exhibit an increasing trend.

Study of shear Alfve’n waves with Landau quantization effect in degenerate relativistic plasma

In a ground breaking endeavor, we investigate a fundamental quantum property of fermions, specifically electrons, within a non-uniform quantized magnetic field, unveiling novel insights into shear Alfve’n waves in the relativistic realm of quantum plasma, particularly within the context of a degenerate Fermi gas. Employing the quantum magnetohydrodynamic model, we delve into the profound implications of the Landau quantization effect. This quantum phenomenon holds paramount importance across diverse fields such as condensed matter physics, astrophysics, and quantum information. Our study focuses on a plasma composed of degenerate relativistic electrons coexisting with cold fluid ions, which are non-degenerate particles. The findings of this research reveal substantial modifications in the thermodynamic, kinetic, and dispersion relation characteristics of shear Alfve’n waves when subjected to a non-uniform quantized magnetic field. This exploration offers a pioneering perspective on the intricate interplay between quantum physics and plasma dynamics, with implications for a wide array of scientific disciplines.