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.     

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.     

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.     

Can the Past Be Changed?

The paper shows that the past, history in a non-technical sense, can be changed in quantum mechanics. The first part of the paper reviews Deutsch's analysis in his paper of 1991. It is demonstrated that Deutsch assumes the existence of a multiplicity of essentially classical worlds. Such a multiplicity of worlds would allow the past to be changed in classical mechanics. It is argued that the existence of multiple classical worlds is not required by quantum mechanics. It is then shown that it is possible to change the past in conventional quantum mechanics even without the assumption of a multiplicity of worlds.     

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.     

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.     

Can Quintessence Be the Rolling Tachyon？

In the light of the recent works by Sen(hep-th/o203211,hep-th/0203265,hep-th/0204143)and Gibbons(hepth/0204008),we present a phase-plane analysis on the cosmology containing a rolling tachyon field in a potential resulting from string theory.we show that there is no stable point on the phase-plane,which indicates that there is a coincidence problem if we consider the tachyon as a candidate for quintessence.Furthermore,we also analyse the phase-plane of the cosmology cotaining a rolling tachyon field for an exactly solvable toy potential in which the critical point is stable.Therefore,it is possible for the rolling tachyon to be a candidate for quintessence if we give up the strict constraint on the potential or find a more appropriate effective potential for the tachyon from M/String theory.     

Scaling Approach to the Growth Equation with a Generalized Conservation Law

The Flory-type scaling approach proposed by Hentschel and Family [Phys. Rev. Lett. 66 (1991) 1982] isgeneralized to the analysis of the growth equation with a generalized conservation law, which contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and molecular-beam epitaxy growth equations as special cases and allows for aunified investigation of growth equations. The scaling exponents obtained here can be in agreement well with thecorresponding results derived by the dynamic renormalization group theory and the previous scaling analvses.     

Why the Mittag-Leffler Function Can Be Considered the Queen Function of the Fractional Calculus?

In this survey we stress the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus. We first start with the analytical properties of the classical Mittag-Leffler function as derived from being the solution of the simplest fractional differential equation governing relaxation processes. Through the sections of the text we plan to address the reader in this pathway towards the main applications of the Mittag-Leffler function that has induced us in the past to define it as the Queen Function of the Fractional Calculus. These applications concern some noteworthy stochastic processes and the time fractional diffusion-wave equation We expect that in the next future this function will gain more credit in the science of complex systems. Finally, in an appendix we sketch some historical aspects related to the author’s acquaintance with this function.     

Can QCD Be a Perturbation Theory of Hadrons?

We have found that the S-matrix for atoms and hadrons depends on a gauge as the elementary particles are off mass-shell in the bound states. The S-matrix for bound states one should to construct by the projection of the Belinfante energy-momentum tensor on the Gauss equation solution for the time component with the time-axis chosen as the eigenvector of the bound state total momentum operator. We have shown that this QCD Hamiltonian determined in infrared region by the rising potential ansatz, besides the parton model in the specific gauge, contains also the nonrelativistic potential model for heavy quarkonia, the chiral Lagrangians for light quarkonia with their spectrum, the glueball physics, and the small effective coupling constant in the whole region of transversal momenta.     

The Second Law of Thermodynamic in Quantum System

The second law of thermodynamics is one of the most fundamental and for-reaching laws of physics. It teaches us that when a closed system undergoes a thermodynamic process the entropy of the system never decreases; it increases, or at least remains constant. If the entropy increases the thermodynamic process is irreversible, otherwise it is reversible. Only ideal thermal process is reversible. In classical world a great number of facts have proved the second law is true. But in quantum world since the quantum coherence and correlations exist we are not sure the second law is still true, at least in principle. This is because that： 1. on the microscopic level the irreversibility is conflict with the reversibility of all fundamental physical laws ; 2. there are not enough evidences to show it is true in quantum world.     

How the Brain Becomes the Mind: Can Thermodynamics Explain the Emergence and Nature of Emotions?

The neural systems’ electric activities are fundamental for the phenomenology of consciousness. Sensory perception triggers an information/energy exchange with the environment, but the brain’s recurrent activations maintain a resting state with constant parameters. Therefore, perception forms a closed thermodynamic cycle. In physics, the Carnot engine is an ideal thermodynamic cycle that converts heat from a hot reservoir into work, or inversely, requires work to transfer heat from a low- to a high-temperature reservoir (the reversed Carnot cycle). We analyze the high entropy brain by the endothermic reversed Carnot cycle. Its irreversible activations provide temporal directionality for future orientation. A flexible transfer between neural states inspires openness and creativity. In contrast, the low entropy resting state parallels reversible activations, which impose past focus via repetitive thinking, remorse, and regret. The exothermic Carnot cycle degrades mental energy. Therefore, the brain’s energy/information balance formulates motivation, sensed as position or negative emotions. Our work provides an analytical perspective of positive and negative emotions and spontaneous behavior from the free energy principle. Furthermore, electrical activities, thoughts, and beliefs lend themselves to a temporal organization, an orthogonal condition to physical systems. Here, we suggest that an experimental validation of the thermodynamic origin of emotions might inspire better treatment options for mental diseases.     

Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems. We show that the time average of the observation function which is not the L ¹(m) function, whose average with respect to the invariant measure m is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.     

Can Torsion Play a Role in Angular Momentum Conservation Law?

In Einstein-Cartan theory, by the use of thegeneral Noether theorem, the general covariantangular-momentum conservation law is obtained withrespect to the local Lorentz transformations. Thecorresponding conservative Noether current is interpreted asthe angular momentum tensor of the gravity-matter systemincluding the spin density. It is pointed out that,assuming the tetrad transformation given by eq. (15), then torsion does not play a role in theconservation law of angular momentum.     

The Pauli Exclusion Principle. Can It Be Proved?

The modern state of the Pauli exclusion principle studies is discussed. The Pauli exclusion principle can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is a so-called spin-statistics connection. The reasons why the spin-statistics connection exists are still unknown, see discussion in text. On the other hand, according to the Pauli exclusion principle, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, all other types of permutation symmetry are forbidden; although the solutions of the Schrödinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the Pauli exclusion principle in some textbooks on quantum mechanics are incorrect and, in general, the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusion principle. Heuristic arguments are given in favor that the existence in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of the degenerate permutation states by the Pauli exclusion principle follows from the general physical assumptions underlying quantum theory.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.     

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.