Information Erasure and the Generalized Second Law of Black Hole Thermodynamics

We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer’s principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer’s principle.     

Generalized Second Law of Thermodynamics in Extended Theories of Gravity

By employing the general expression for temperature associated with the apparent horizon of FRW universe and assuming a region of an expanding universe enclosed by the apparent horizon as a thermal system in equilibrium, we are able to show that the generalized second law of thermodynamics holds in Gauss-Bonnet and more general Lovelock gravities.     

Accretion of Phantom Energy and Generalized Second Law of Thermodynamics for Einstein-Maxwell-Gauss-Bonnet Black Hole

We have investigated the accretion of phantom energy onto a 5-dimensional extreme Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole. It is shown that the evolution of the EMGB black hole mass due to phantom energy accretion depends only on the pressure and density of the phantom energy and not on the black hole mass. Further we study the generalized second law of thermodynamics (GSL) at the event horizon and obtain a lower bound on the pressure of the phantom energy.     

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system     

Inertial Effects in Nonequilibrium Work Fluctuations by a Path Integral Approach

Inertial effects in fluctuations of the work to sustain a system in a nonequilibrium steady state are discussed for a dragged massive Brownian particle model using a path integral approach. We calculate the work distribution function in the laboratory and comoving frames and prove the asymptotic fluctuation theorem for these works for any initial condition. Important and observable differences between the work fluctuations in the two frames appear for finite times and are discussed concretely for a nonequilibrium steady state initial condition. We also show that for finite times a time oscillatory behavior appears in the work distribution function for masses larger than a nonzero critical value.     

Non-Equilibrium Thermodynamics and Topology of Currents

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged quantities which describe such stochastic maps, in particular time-averaged currents and density functionals. We derive the large deviations principle for these quantities, as well as for global topological currents, and formulate variational, thermodynamic relations to establish large deviation properties of the topological currents. We illustrate the theory with a nontrivial example of a Heisenberg spin-chain with a topological driving of the Wess-Zumino type. The Cramér functional of the topological current is found explicitly in the instanton gas regime for the spin-chain model in the weak-noise limit. In the context of the Morse theory, we discuss a general reduction of continuous stochastic models with weak noise to effective Markov chains describing transitions between stable fixed points.     

Mechanism of Formation of Prandtl’s Secondary Flows of the Second Kind

Doklady Physics - Turbulent flow in a tube of square cross section is investigated numerically. The concentrated longitudinal vortices responsible for the occurrence of secondary flows are studied....     

A Precise Formulation of the Third Law of Thermodynamics

The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature  Γ₀  are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or “by a finite number of operations”), it admits as corollary, under a continuity assumption, that all points of  Γ₀  are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.     

Finite-Time Fluctuations in the Degree Statistics of Growing Networks

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barabási-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.     

Can Quantum Correlations Lead to Violation of the Second Law of Thermodynamics?

Quantum entanglement can cause the efficiency of a heat engine to be greater than the efficiency of the Carnot cycle. However, this does not mean a violation of the second law of thermodynamics, since there is no local equilibrium for pure quantum states, and, in the absence of local equilibrium, thermodynamics cannot be formulated correctly. Von Neumann entropy is not a thermodynamic quantity, although it can characterize the ordering of a system. In the case of the entanglement of the particles of the system with the environment, the concept of an isolated system should be refined. In any case, quantum correlations cannot lead to a violation of the second law of thermodynamics in any of its formulations. This article is devoted to a technical discussion of the expected results on the role of quantum entanglement in thermodynamics.     

Lee–Yang Theorems and the Complexity of Computing Averages

We study the complexity of computing average quantities related to spin systems, such as the mean magnetization and susceptibility in the ferromagnetic Ising model, and the average dimer count (or average size of a matching) in the monomer-dimer model. By establishing connections between the complexity of computing these averages and the location of the complex zeros of the partition function, we show that these averages are #P-hard to compute, and hence, under standard assumptions, computationally intractable. In the case of the Ising model, our approach requires us to prove an extension of the famous Lee–Yang Theorem from the 1950s.     

On the Second Fluctuation–Dissipation Theorem for Nonequilibrium Baths

Baths produce friction and random forcing on particles suspended in them. The relation between noise and friction in (generalized) Langevin equations is usually referred to as the second fluctuation–dissipation theorem. We show what is the proper nonequilibrium extension, to be applied when the environment is itself active and driven. In particular we determine the effective Langevin dynamics of a probe from integrating out a steady nonequilibrium environment. The friction kernel picks up a frenetic contribution, i.e., involving the environment’s dynamical activity, responsible for the breaking of the standard Einstein relation.     

A formal treatment of the consequences of the Second Law of Thermodynamics in Carathéodory's formulation

The consequences of the Second Law of Thermodynamics, as enunciated in the Principle of Carathéodory, are developed by means of a largely formal argument. The need for the introduction of the Theorem of Carathéodory does not arise. One virtue of the method is the immediacy with which it leads to the Principle of Increase of Entropy.     

Nonequilibrium Layer in the Crust of Neutron Stars and Nonequilibrium β-Processes in Astrophysics

Journal of Experimental and Theoretical Physics - The formation of the chemical composition of neutron star envelopes, at densities 1010–1013 g cm–3, is considered. As hot matter is...     

The Generalized Second Law of Thermodynamics of?the?Universe Bounded by the Event Horizon and?Modified Gravity Theories

In this paper, we investigate the validity of the generalized second law of thermodynamics of the universe bounded by the event horizon. Here we consider homogeneous and isotropic model of the universe filled with perfect fluid in one case and in another case holographic model of the universe has been considered. In the third case the matter in the universe is taken in the form of non-interacting two fluid system as holographic dark energy and dust. Here we study the above cases in the Modified gravity, f(R) gravity.     

Annihilation of Vertical-Bloch-Line Chains in the Walls of the Second Kind of Dumbbell Domains Subjected to Joint Static Bias Field and In-Plane Field

Using equations governing the variation of the beam size and the curvature of wave front in the logarithmically saturable nonlinear media, the Gaussian-type breath mode of spatial soliton has been described in detail. With the aid of a potential method, the positive and negative signs can be assigned to the first order derivative of the beam size with respect to the propagation distance. Thus, important parameters of the breath mode, such as the beam size, curvatwre radius of the wave front, the period, etc., have been calculated.     

Generalized Second Law of Thermodynamics for?Interacting Dark Energy in the DGP Braneworld

In this paper, we investigate the validity of the generalized second law of thermodynamics (GSLT) in the DGP braneworld when the universe is filled with interacting two fluid system: one in the form of cold dark matter and other is holographic dark energy. The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon or the event horizon. The universe is chosen to be homogeneous and isotropic FRW model and the validity of the first law has been assumed here.