اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEquality statements for entropy change in open systems
277
0
0.0
(
0
)
تأليف
John M. Robinson
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The entropy change of a (non-equilibrium) Markovian ensemble is calculated from (1) the ensemble phase density $p(t)$ evolved as iterative map, $p(t) = mathbb{M}(t) p(t- Delta t)$ under detail balanced transition matrix $mathbb{M}(t)$, and (2) the invariant phase density $pi(t) = mathbb{M}(t)^{infty} pi(t) $. A virtual measurement protocol is employed, where variational entropy is zero, generating exact expressions for irreversible entropy change in terms of the Jeffreys measure, $mathcal{J}(t) = sum_{Gamma} [p(t) - pi(t)] ln bfrac{p(t)}{pi(t)}$, and for reversible entropy change in terms of the Kullbach-Leibler measure, $mathcal{D}_{KL}(t) = sum_{Gamma} pi(0) ln bfrac{pi(0)}{pi(t)}$. Five properties of $mathcal{J}$ are discussed, and Clausius theorem is derived.
قيم البحث
اقرأ أيضاً
We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the chemical potentia
l is constant in the two sets of parallel formalisms, where the fundamental thermodynamic equations with dual interpretations of thermodynamic quantities are derived for the open systems. By introducing parallel structures of Legendre transformations, other thermodynamic equations with dual interpretations of quantities are also deduced in the open systems, and then several dual thermodynamic relations are inferred. One can easily find that there are correlations between the dual relations, from which an equivalent rule is found that the Tsallis factor is invariable in calculations of partial derivative with constant volume or constant entropy. Using this rule, more correlations can be found. And the statistical expressions of the Lagrange internal energy and pressure are easily obtained.
We formulate a new ``Wigner characteristics based method to calculate entanglement entropies of subsystems of Fermions using Keldysh field theory. This bypasses the requirements of working with complicated manifolds for calculating R{e}nyi entropies
for many body systems. We provide an exact analytic formula for R{e}nyi and von-Neumann entanglement entropies of non-interacting open quantum systems, which are initialised in arbitrary Fock states. We use this formalism to look at entanglement entropies of momentum Fock states of one-dimensional Fermions. We show that the entanglement entropy of a Fock state can scale either logarithmically or linearly with subsystem size, depending on whether the number of discontinuities in the momentum distribution is smaller or larger than the subsystem size. This classification of states in terms number of blocks of occupied momenta allows us to analytically estimate the number of critical and non-critical Fock states for a particular subsystem size. We also use this formalism to describe entanglement dynamics of an open quantum system starting with a single domain wall at the center of the system. Using entanglement entropy and mutual information, we understand the dynamics in terms of coherent motion of the domain wall wavefronts, creation and annihilation of domain walls and incoherent exchange of particles with the bath.
We study thermalization in open quantum systems using the Lindblad formalism. A method that both thermalizes and couples to Lindblad operators only at edges of the system is introduced. Our method leads to a Gibbs state of the system, satisfies fluct
uation-dissipation relations, and applies both to integrable and non-integrable systems. Possible applications of the method include the study of systems coupled locally to multiple reservoirs. Our analysis also highlights the limits of applicability of the Lindblad approach to study strongly driven systems.
We demonstrate the accurate calculation of entropies and free energies for a variety of liquid metals using an extension of the two phase thermodynamic (2PT) model based on a decomposition of the velocity autocorrelation function into gas-like (hard
sphere) and solid-like (harmonic) subsystems. The hard sphere model for the gas-like component is shown to give systematically high entropies for liquid metals as a direct result of the unphysical Lorentzian high-frequency tail. Using a memory function framework we derive a generally applicable velocity autocorrelation and frequency spectrum for the diffusive component which recovers the low frequency (long time) behavior of the hard sphere model while providing for realistic short time coherence and high frequency tails to the spectrum. This approach provides a significant increase in the accuracy of the calculated entropies for liquid metals and is compared to ambient pressure data for liquid sodium, aluminum, gallium, tin, and iron. The use of this method for the determination of melt boundaries is demonstrated with a calculation of the high pressure bcc melt boundary for sodium. With the significantly improved accuracy available with the memory function treatment for softer interatomic potentials, the 2PT model for entropy calculations should find broader application in high energy density science, warm dense matter, planetary science, geophysics, and material science.
We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are compared with th
e results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
