Large Deviations and¶Variational Principle for Harmonic Crystals

We consider massless Gaussian fields with covariance related to the Green function of a long range random walk on Ê^d. These are viewed as Gibbs measures for a linear-quadratic interaction. We establish thermodynamic identities and prove a version of Gibbs' variational principle, showing that translation invariant Gibbs measures are characterized as minimizers of the relative entropy density. We then study the large deviations of the empirical field of a Gibbs measure. We show that a weak large deviation principle holds at the volume order, with rate given by the relative entropy density.     

Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

We solve the Schr?dinger equation with a position-dependent mass(PDM) charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov–Bohm(AB) flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.     

Thermodynamics of Reduced State of the Field

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.     

Fluctuations of Entanglement Entropy in Noninertial Frames

The fluctuation and relative fluctuation of entanglement entropy of a bipartite system for Dirac fields in noninertial frames are investigated. It is shown that the fluctuation and relative fluctuation of entanglement entropy are observer-dependent, which depend on their observed frames. It is found that both the fluctuation and relative fluctuation of entanglement entropy become more noticeable with the increasing of the subsystem's acceleration. We also find that the entanglement entropy always has fluctuation regardless of the initial state parameter and for any magnitude of the acceleration. We argue that the statistical mean for the measurement of entanglement entropy relates to the accelerated motion of the observer.     

Fluctuations of Entanglement Entropy in Noninertial Frames

The fluctuation and relative fluctuation of entanglement entropy of a bipartite system for Dirac fields in noninertial frames are investigated. It is shown that the fluctuation and relative fluctuation of entanglement entropy are observer-dependent, which depend on their observed frames. It is found that both the fluctuation and relative fluctuation of entanglement entropy become more noticeable with the increasing of the subsystem's acceleration. We also find that the entanglement entropy always has fluctuation regardless of the initial state parameter and for any magnitude of the acceleration. We argue that the statistical mean for the measurement of entanglement entropy relates to the accelerated motion of the observer.     

Entangled states in the two-mode coherent fields interacting with a two-level atom

We investigate the entanglement properties of the two-mode coherent fields interacting with a two-level atom via the two-photon transition. We discuss the quantum entanglement between the two-mode coherent fields and the two-level atom by using the quantum reduced entropy and that between the two-mode coherent fields by using the quantum relative entropy. We also examine the influences of the initial states of the atom and the two-mode coherent fields on the quantum entanglement of the system. Our results show that three types of entangled states can be prepared via the two-mode coherent fields interacting with a two-level atom and choosing appropriately the initial-state parameters of the system.     

Fluctuation theorem for entropy production at strong coupling

Fluctuation theorems have been applied successfully to any system away from thermal equilibrium, which are helpful for understanding the thermodynamic state evolution. We investigate fluctuation theorems for strong coupling between a system and its reservoir, by path-dependent definition of work and heat satisfying the first law of thermodynamics. We present the fluctuation theorems for two kinds of entropy productions. One is the informational entropy production, which is always non-negative and can be employed in either strong or weak coupling systems. The other is the thermodynamic entropy production, which differs from the informational entropy production at strong coupling by the effects regarding the reservoir. We find that, it is the negative work on the reservoir, rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling. Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.     

Entropy in Kerr–de Sitter Black Holes with Spin Fields

Generalized master equations due to spin fields are given. We obtain the entropy of electromagnetic, gravitational, Dirac, and scalar fields in a unified form by using the improved brick-wall method—membrane model. The results show that, as the cutoff is properly chosen, the entropy in the black hole satisfies the Bekenstein–Hawking area formula.     

Entropy production in nonequilibrium systems at stationary states

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.     

An exactly solvable two-dimensional biomembrane model

A model for a two-dimensional lipid bilayer, in which both short-range repulsive forces and long-range attractive forces piay a role, is solved exactly. First, in the absence of attractive forces, the configurational entropy is calculated by restricting the lipid hydrocarbon tails to a lattice and solving the resulting counting problem exactly. When long-range attractive forces which decrease exponentially with distance are acting between the polar head groups of the lipids, the partition function can still be calculated exactly, using integration over Gaussian random fields. The thermodynamic functions show a singularity which reflects the completion of the process of self-assemblage of the lipid bilayer. Finally, the model is used to test an approximation method for lipid bilayers.     

From Nonlinear Scaling Fields to Critical Amplitudes

We propose to combine the nonlinear scaling fields associated with the high-temperature (HT) fixed point, with those associated with the unstable fixed point, in order to calculate the susceptibility and other thermodynamic quantities. The general strategy relies on simple linear relations between the HT scaling fields and the thermodynamic quantities, and the estimation of RG invariants formed out of the two sets of scaling fields. This estimation requires convergent expansions in overlapping domains. If, in addition, the initial values of the scaling fields associated with the unstable fixed point can be calculated from the temperature and the parameters appearing in the microscopic Hamiltonian, one can estimate the critical amplitudes. This strategy has been developed using Dyson's hierarchical model where all the steps can be approximately implemented with good accuracy. We show numerically that for this model (and a simplified version of it), the required overlap apparently occurs, allowing an accurate determination of the critical amplitudes.     

Gaussian Fields and Random Packing

Consider sequential packing of unit volume balls in a large cube, in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a Gaussian field in the thermodynamic limit. The results cover related applied models, including ballistic deposition and spatial birth-growth models.     

Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction

A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we study both the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators, the multi-point Maximum A-Posteriori (MAP) estimators, an efficient class of multi-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators, and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring.     

Entropy and correlators in quantum field theory

It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.     

Hamiltonian and Thermodynamic Modeling of Quantum Turbulence

The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity, all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure developed in ⁴He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with thermodynamics, and (ii) it is used as a guide in the construction of the novel model.     

Entanglement properties in a system of a pairwise entangled state

Based on the quantum information theory, this paper has investigated the entanglement properties of a system which is composed of the two entangled two-level atoms interacting with the two-mode entangled coherent fields. The influences of the strength of light field and the two parameters of entanglement between the two-mode fields on the field entropy and on the negative eigenvalues of partial transposition of density matrix are discussed by using numerical calculations. The result shows that the entanglement properties in a system of a pairwise entangled states can be controlled by appropriately choosing the two parameters of entanglement between the two-mode entangled coherent fields and the strength of two light fields respectively.     

Dissipation of ‘dark energy’ by cortex in knowledge retrieval

We have devised a thermodynamic model of cortical neurodynamics expressed at the classical level by neural networks and at the quantum level by dissipative quantum field theory. Our model is based on features in the spatial images of cortical activity newly revealed by high-density electrode arrays. We have incorporated the mechanism and necessity for so-called dark energy in knowledge retrieval. We have extended the model first using the Carnot cycle to define our measures for energy, entropy and temperature, and then using the Rankine cycle to incorporate criticality and phase transitions. We describe the dynamics of two interactive fields of neural activity that express knowledge, one at high and the other at low energy density, and the two operators that create and annihilate the fields. We postulate that the extremely high density of energy sequestered briefly in cortical activity patterns can account for the vividness, richness of associations, and emotional intensity of memories recalled by stimuli.     

Topological Entanglement Entropy from the Holographic Partition Function

We study the entropy of chiral 2+01-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. We give a general expression for the holographic partition function, and discuss several examples in depth, including abelian and non-abelian fractional quantum Hall states, and $p+ip$ superconductors. We extend these results to include a point contact allowing tunneling between two points on the edge, which causes thermodynamic entropy associated with the point contact to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and we can identify the thermodynamic entropy loss with the loss of the edge entanglement entropy. From these results, we obtain a simple interpretation of the non-integer ‘ground state degeneracy’ which is obtained in 1+1-dimensional quantum impurity problems: its logarithm is a 2+1-dimensional topological entanglement entropy.     

On thermodynamics of RN-dS black hole surrounded by the quintessence

De Sitter black holes have the black hole horizon and the cosmological horizon, and the thermodynamic quantities on the two horizons all satisfy the first law of thermodynamics. The thermodynamic quantities on the two horizons are not independent but are correlated to each other. Taking de Sitter space-time as thermodynamic system, we investigated the effective thermodynamic quantities of Reissner–Nordström de Sitter black hole surrounded by the quintessence (RN-DSQ). We obtained the effective temperature and entropy of the system by considering the corrections between the black hole horizon and the cosmological horizon. We found that the entropy of the RN-DSQ is in agreement with that of Reissner–Nordström de Sitter black hole. It offers a basis for further studying of the thermodynamic properties of de Sitter space-time.