Entropy defect in thermodynamics Livadiotis, George; McComas, David J
Scientific reports,
06/2023, Letnik:
13, Številka:
1
Journal Article
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This paper describes the physical foundations of the newly discovered "entropy defect" as a basic concept of thermodynamics. The entropy defect quantifies the change in entropy caused by the order ...induced in a system through the additional correlations among its constituents when two or more subsystems are assembled. This defect is closely analogous to the mass defect that arises when nuclear particle systems are assembled. The entropy defect determines how the entropy of the system compares to its constituent's entropies and stands on three fundamental properties: each constituent's entropy must be (i) separable, (ii) symmetric, and (iii) bounded. We show that these properties provide a solid foundation for the entropy defect and for generalizing thermodynamics to describe systems residing out of the classical thermal equilibrium, both in stationary and nonstationary states. In stationary states, the consequent thermodynamics generalizes the classical framework, which was based on the Boltzmann-Gibbs entropy and Maxwell-Boltzmann canonical distribution of particle velocities, into the respective entropy and canonical distribution associated with kappa distributions. In nonstationary states, the entropy defect similarly acts as a negative feedback, or reduction of the increase of entropy, preventing its unbounded growth toward infinity.
Abstract
We analyze proton bulk parameters derived from Ulysses observations and investigate the polytropic behavior of solar wind protons over a wide range of heliocentric distances and latitudes. ...The large-scale variations of the proton density and temperature over heliocentric distance indicate that plasma protons are governed by subadiabatic processes (polytropic index
γ
< 5/3), if we assume protons with three effective kinetic degrees of freedom. From the correlation between the small-scale variations of the plasma density and temperature in selected subintervals, we derive a polytropic index
γ
∼ 1.4 on average. Further examination shows that the polytropic index does not have an apparent dependence on the solar wind speed. This agrees with the results of previous analyses of solar wind protons at ∼1 au. We find that the polytropic index varies slightly over the range of the heliocentric distances and heliographic latitudes explored by Ulysses. We also show that the homogeneity of the plasma and the accuracy of the polytropic model applied to the data points vary over Ulysses' orbit. We compare our results with the results of previous studies that derive the polytropic index of solar wind ions within the heliosphere using observations from various spacecraft. We finally discuss the implications of our findings in terms of heating mechanisms and the effective degrees of freedom of the plasma protons.
This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and ...shows their connection with the formalism of kappa distributions. By defining the "entropy defect" in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm.
Abstract
Fast solar wind (SW) flows outward from polar coronal holes (PCHs). The latitudinal extent of the fast SW varies during different phases of the solar cycle. The fast SW in the inner ...heliosheath produces a flatter proton spectrum than the slow SW that can be observed through energetic neutral atoms (ENAs) by the Interstellar Boundary Explorer (IBEX). In this study, we investigate the evolution of PCHs as reflected in the high-time resolution ENA flux measurements from IBEX-Hi, where the PCHs are identified by ENA spectral indices <1.8. The ENA spectral index over the poles shows a periodic evolution over the solar cycle 24. The surface area with flatter ENA spectra (<1.8) around the ecliptic south pole increases slightly from 2009–2011 and then decreased gradually from 2012–2014. The PCH completely disappears in 2016 and then starts to appear again starting in 2017, gradually growing until 2019. This evolution shows a clear correlation with the change in the PCH area observed at the Sun once the delay in the ENA observation time is included. In addition, the higher-cadence ENA data at the highest latitudes show a rapid evolution of the ENA spectrum near the south pole in 2014 and 2017. The rapid evolution in 2014 is related to a rapid
closing
of PCHs in 2012 and that in 2017 is related to a rapid
opening
of PCHs in late 2014. These results also agree qualitatively with the evolution of the ENA spectral index from simulations using a simple time-dependent heliospheric flow model.
Abstract
This study provides a detailed analysis of five distant interplanetary shocks observed by the Solar Wind Around Pluto instrument on board New Horizons, which exhibit the signature of a ...suprathermal H
+
pickup ion (PUI) tail in the downstream distribution. These shocks were observed with a PUI data cadence of approximately 24 hr, covering a heliocentric distance range of 23.71–36.75 au. The shock compression ratio varies between approximately 1.4 and 3.2. The H
+
PUI density and temperature show a gradual increase across the shock, while the H
+
solar wind density shows erratic behavior without a distinct downstream compression. The H
+
PUI cooling index variation across the shock displays different characteristics in each shock. This study demonstrates, for the first time, the variation of the number density of downstream H
+
PUI tails with the shock compression ratio, revealing an increase in tail density with stronger shocks. Additionally, theoretical estimates of reflected PUI number densities derived from the electrostatic cross-shock potential agree very well with the observed H
+
PUI tail densities for stronger shocks.
Abstract
Nearly incompressible magnetohydrodynamic (NI MHD) theory for
β
∼ 1 (or
β
≪ 1) plasma has been developed and applied to the study of solar wind turbulence. The leading-order term in
β
∼ 1 or
...β
≪ 1 plasma describes the majority of 2D turbulence, while the higher-order term describes the minority of slab turbulence. Here, we develop new NI MHD turbulence transport model equations in the high plasma beta regime. The leading-order term in a
β
≫ 1 plasma is fully incompressible and admits both structures (flux ropes or magnetic islands) and slab (Alfvén waves) fluctuations. This paper couples the NI MHD turbulence transport equations with three fluid (proton, electron, and pickup ion) equations, and solves the 1D steady-state equations from 1–75 au. The model is tested against 27 yr of Voyager 2 data, and Ulysses and NH SWAP data. The results agree remarkably well, with some scatter, about the theoretical predictions.
Abstract Energetic neutral atoms (ENAs) from the heliosphere are a unique means to remotely image the boundary regions of our heliosphere. The Interstellar Boundary Explorer (IBEX) has been very ...successful in measuring these ENAs since 2008 at energies from tens of eV to 6 keV. The main question raised by one solar cycle of IBEX-Lo observations at 0.05–2 keV is the strong and ubiquitous underestimation of several model predictions compared with actually measured ENA intensities at energies between 100 and 500 eV. This study converts the observed ENA intensities into plasma pressures for different sky directions and considers the implications for our understanding of the heliosheath and the source of the observed ENAs.
•The Alice instrument on New Horizons measured a UV solar occultation by Pluto's atmosphere in 2015.•Densities were derived for N2, CH4, C2H2, C2H4, C2H6, and haze.•These imply low escape rates ...(CH4-dominated), a stable lower atmosphere, direct evidence for C2Hx photochemistry, and haze whose extinction coefficient is roughly proportional to N2 density.
The Alice instrument on NASA's New Horizons spacecraft observed an ultraviolet solar occultation by Pluto's atmosphere on 2015 July 14. The transmission vs. altitude was sensitive to the presence of N2, CH4, C2H2, C2H4, C2H6, and haze. We derived line-of-sight abundances and local number densities for the 5 molecular species, and line-of-sight optical depth and extinction coefficients for the haze. We found the following major conclusions: (1) We confirmed temperatures in Pluto's upper atmosphere that were colder than expected before the New Horizons flyby, with upper atmospheric temperatures near 65–68 K. The inferred enhanced Jeans escape rates were (3–7) × 1022 N2 s−1 and (4–8) × 1025 CH4 s−1 at the exobase (at a radius of ∼ 2900 km, or an altitude of ∼1710 km). (2) We measured CH4 abundances from 80 to 1200 km above the surface. A joint analysis of the Alice CH4 and Alice and REX N2 measurements implied a very stable lower atmosphere with a small eddy diffusion coefficient, most likely between 550 and 4000 cm2 s−1. Such a small eddy diffusion coefficient placed the homopause within 12 km of the surface, giving Pluto a small planetary boundary layer. The inferred CH4 surface mixing ratio was ∼ 0.28–0.35%. (3) The abundance profiles of the “C2Hx hydrocarbons” (C2H2, C2H4, C2H6) were not simply exponential with altitude. We detected local maxima in line-of-sight abundance near 410 km altitude for C2H4, near 320 km for C2H2, and an inflection point or the suggestion of a local maximum at 260 km for C2H6. We also detected local minima near 200 km altitude for C2H4, near 170 km for C2H2, and an inflection point or minimum near 170–200 km for C2H6. These compared favorably with models for hydrocarbon production near 300–400 km and haze condensation near 200 km, especially for C2H2 and C2H4 (Wong et al., 2017). (4) We found haze that had an extinction coefficient approximately proportional to N2 density.
The Magnetospheric Multiscale (MMS) spacecraft obtained unprecedented high‐time resolution multipoint particle and field measurements of an interplanetary shock event on 8 January 2018. The ...spacecraft encountered the supercritical forward shock of a forward/reverse shock pair in the pristine solar wind upstream of the bow shock near the subsolar point as they neared apogee at ~25 RE. The high‐time resolution measurements from the four spacecraft, separated by only ~20 km, allowed direct measurement of particle distributions revealing evidence of electron heating and near specularly reflected ions. The cross‐shock potential is calculated directly from 3‐D electric field measurements. This is the first reported direct high temporal resolution (<1 s) observation at an interplanetary shock of near specularly reflected ions. Calculation of the cross‐shock potential yields a potential jump significant enough to reflect at least some of the protons from the incident solar wind beam. The cross‐shock potential calculated here is consistent with previous estimations based on particle measurements and numerical/analytical simulations. The ambipolar contribution to the cross‐shock potential calculated from the four‐spacecraft divergence of the electron pressure tensor is somewhat higher than that inferred form the Liouville‐mapped electron energy gain across the shock. Furthermore, the high‐time‐resolution 3‐D electric field measurements reported here reveal small‐scale nonlinear structures embedded in the shock layer that contribute to the nonmonotonic shock transition.
Key Points
MMS observed a supercritical IP shock in the upstream pristine solar wind, directly resolving near specularly reflected ions
The cross‐shock potential jump calculated from 3‐D E‐field measurements is consistent with the observed electron heating and ion reflection
The high‐temporal‐resolution 3‐D electric field measurements revealed small‐scale nonlinear structures embedded within the shock front
Direct-sampling observations of interstellar neutral (ISN) He by the Interstellar Boundary Explorer (IBEX) provide valuable insight into the physical state of and processes operating in the ...interstellar medium ahead of the heliosphere. The ISN He atom signals are observed at the four lowest ESA steps of the IBEX-Lo sensor. The observed signal is a mixture of the primary and secondary components of ISN He and H. Previously, only data from one of the ESA steps have been used. Here, we extend the analysis to data collected in the three lowest ESA steps with the strongest ISN He signal, for the observation seasons 2009-2015. The instrument sensitivity is modeled as a linear function of the atom impact speed onto the sensor's conversion surface separately for each ESA step of the instrument. We find that the sensitivity increases from lower to higher ESA steps, but within each of the ESA steps it is a decreasing function of the atom impact speed. This result may be influenced by the hydrogen contribution, which was not included in the adopted model, but seems to exist in the signal. We conclude that the currently accepted temperature of ISN He and velocity of the Sun through the interstellar medium do not need a revision, and we sketch a plan of further data analysis aiming at investigating ISN H and a better understanding of the population of ISN He originating in the outer heliosheath.
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