Information-Probabilistic Description of the Universe

We describe the universe as a single entangled ensemble of quantum particles. The total entropy of this world ensemble, which can be expressed as a sum of information, thermodynamic and entanglement components, is assumed to be always zero. This condition suggests information quantization, which we associate with the Planck’s action. Then the entropy neutrality condition for the universe leads to the zero-action principle. We show that the main concepts of classical space-time and gravity naturally emerge in this picture. A generalized least action principle, which embraces the maximal entropy principles of information theory, is introduced.     

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic "Landau" potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.     

Uncertainty relations with quantum memory for the Wehrl entropy

We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with a given conditional von Neumann entropy and proves that this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The second relation applies to the tripartite memory scenario. It determines the minimum of the sum of the Wehrl entropy of a quantum state conditioned on the first memory quantum system with the Wehrl entropy of the same state conditioned on the second memory quantum system and proves that also this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The Wehrl entropy of a quantum state is the Shannon differential entropy of the outcome of a heterodyne measurement performed on the state. The heterodyne measurement is one of the main measurements in quantum optics and lies at the basis of one of the most promising protocols for quantum key distribution. These fundamental entropic uncertainty relations will be a valuable tool in quantum information and will, for example, find application in security proofs of quantum key distribution protocols in the asymptotic regime and in entanglement witnessing in quantum optics.     

Information-theoretic limits of control

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of control systems shows feedback control to be a zero sum game: each bit of information gathered from a dynamical system by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information. Consequences for the control of discrete state systems and chaotic maps are discussed.     

Electronic non-adiabatic transitions derivation of the general adiabatic-diabatic transformation matrix

Simulations generating a statistical ensemble of configurations of a molecular system provide information to derive entropy. For cases where the spatial distribution is bounded, the entropy can be derived from the average of the logarithm of the spatial probability density, but will be subject to systematic errors due to statistical fluctuations. A method is given to eliminate these errors by using different interval sizes and fitting the results to a simple theoretical expression. The method is feasible when the multidimensional case can be broken up into a sum of low dimensional contributions. The validity of the latter approximation and ways to correct for correlations are discussed.     

Entropy balance in distributed reversible Gray-Scott model

A practical way to calculate the entropy change in the distributed media composed of reversible Gray-Scott model is demonstrated. The entropy change is given as the sum of the entropy production and the divergence of entropy flow. The divergence of entropy is calculated based on the chemical potential of steady state. It becomes evident that: (i) the entropy change for the emergence of dissipative structures in the open system can be positive or negative, (ii) most of the entropy produced inside the system is thrown out to the environment when dissipative structures are developing, (iii) the entropy production and the divergence of entropy flow balance completely, when the system shows static steady states, (iv) the entropy change behaves as if it is the time derivative of the entropy production. Prior to these calculations of entropy balance, the features of emergent patterns in the two-dimensional system are examined in terms of entropy production solely. The results imply that the entropy production can be an index for us to discriminate spatial patterns, but is not a global thermodynamic potential for the evolution of dissipative structures.     

Belavkin–Staszewski Relative Entropy,Conditional Entropy,and Mutual Information

Belavkin–Staszewski relative entropy can naturally characterize the effects of the possible noncommutativity of quantum states. In this paper, two new conditional entropy terms and four new mutual information terms are first defined by replacing quantum relative entropy with Belavkin–Staszewski relative entropy. Next, their basic properties are investigated, especially in classical-quantum settings. In particular, we show the weak concavity of the Belavkin–Staszewski conditional entropy and obtain the chain rule for the Belavkin–Staszewski mutual information. Finally, the subadditivity of the Belavkin–Staszewski relative entropy is established, i.e., the Belavkin–Staszewski relative entropy of a joint system is less than the sum of that of its corresponding subsystems with the help of some multiplicative and additive factors. Meanwhile, we also provide a certain subadditivity of the geometric Rényi relative entropy.     

The effect of screening on entropy production in pattern formation

Information theory is used to study the effects of screening on the rate of entropy production during pattern formation. Screening is an effect where the outermost parts of a growing fractal pattern influence the growth probability at interior sites. The results demonstrate that a state of maximum entropy production does exist for dynamical systems which generate patterns based on simple screening rules alone. This state corresponds to a critical point where the pattern exhibits self-similarity and fractal properties typical of random aggregates. Scaling occurs because the screening transmits information from the smallest to the largest scales of the system.     

利用广义不确定关系计算 Reissner-Nordström-de Sitter黑洞的统计力学熵

利用广义不确定关系修正的态密度方程并采用Wentzel-Kramers-Brillouin (WKB) 近似方法, 计算了Reissner-Nordström-de Sitter (RNdS) 黑洞时空中标量场的统计力学熵. 结果表明, 由这种方法得到的黑洞熵与它的内、外视界面积和宇宙视界面积之和成正比, 这与采用其他方法所得的结果一致, 从而揭示了黑洞熵与视界面积之间的内在联系, 也进一步表明了黑洞熵是视界面上量子态的熵, 是一种量子效应.     

利用广义不确定关系计算Reissner-Nordstrm-de Sitter黑洞的统计力学熵

利用广义不确定关系修正的态密度方程并采用Wentzel-Kramers-Brillouin(WKB)近似方法,计算了Reissner-Nordstrm-de Sitter(RNdS)黑洞时空中标量场的统计力学熵.结果表明,由这种方法得到的黑洞熵与它的内、外视界面积和宇宙视界面积之和成正比,这与采用其他方法所得的结果一致,从而揭示了黑洞熵与视界面积之间的内在联系,也进一步表明了黑洞熵是视界面上量子态的熵,是一种量子效应.     

Entropy and topology of the Kerr—de Sitter black hole

By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole is investigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of the Euler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin of the entropy of the black hole is related to the topology of its instanton.     

信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系--兼论玻尔兹曼熵和克劳修斯熵是否等价

论述了信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系;由不涉及具体系统的方法从玻尔兹曼关系、信息熵推导出了克劳修斯熵的表达式;指出玻尔兹曼熵与克劳修斯熵不是等价关系,而是玻尔兹曼熵包含克劳修斯熵,信息熵又包含玻尔兹曼熵。     

Entropy production along a stochastic trajectory and an integral fluctuation theorem

For stochastic nonequilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and entropy production in the surrounding medium. The integrated sum of both Delatas(tot) is shown to obey a fluctuation theorem (exp([-Deltas(tot) = 1 for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval.     

Distribution of Mutual Information in Multipartite States

Using the relative entropy of total correlation, we derive an expression relating the mutual information of n-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations.     

Physical complexity of variable length symbolic sequences

A measure called physical complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism’s genome. It is based on Shannon’s entropy, measuring the information in a population evolved in its environment, by using entropy to estimate the randomness in the genome. It is calculated from the difference between the maximal entropy of the population and the actual entropy of the population when in its environment, estimated by counting the number of fixed loci in the sequences of a population. Up until now, physical complexity has only been formulated for populations of sequences with the same length. Here, we investigate an extension to support variable length populations. We then build upon this to construct a measure for the efficiency of information storage, which we later use in understanding clustering within populations. Finally, we investigate our extended physical complexity through simulations, showing it to be consistent with the original.     

Entropy growth and degradation of entanglement due to phase decoherence in ion traps

We study how phase decoherence through intrinsic decoherence leads to growing entropy and a strong degradation of the maximum generated entanglement as a measure of information content of ionic state due to ion-laser interaction with a trapped ion. We calculate the partial entropy of the particle (atom or trapped ion) and field subsystems as well as the total entropy. The total entropy is shown to increase with time. Thus, the partial field or atomic entropy cannot be used as a direct measure of the particle–field entanglement. We find that, at least qualitatively, the difference between the total entropy and the sum of field and atom partial entropies can be used as an entanglement measure, when compared with an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix. We find a very strong sensitivity of the maximum generated entanglement on the decoherence and the chosen intrinsic decoherence parameter.     

On the Origin of Black-Hole Entropy

A simple statistical interpretation of the origin of black hole entropy is presented. It is shown that this entropy can be understood as emerging as a result of missing information about the exact state of the matter from which the black hole was formed.     

Statistical Entropy of Vaidya-de Sitter Black Hole to All Orders in Planck Length

Considering corrections to all orders in Planck length on the quantum state density from generalized uncertainty principle, we calculate the statistical entropy of scalar field near event horizon and cosmological horizon of Vaidya-de Sitter black hole without any artificial cutoff. It is shown that the entropy is linear sum of event horizon area and cosmological horizon area and there are similar proportional parameters related to changing rate of the horizon position. This is different from the static and stationary cases.     

Dynamical correlations of negativity and entropy for pure and mixed states in two coupled quartic oscillators

Various measures of entanglement have triggered considerable interest in the relationship between entanglement measures and other well-known quantities. As a demonstration, the dynamical correlation of negativity and entropy is studied in two coupled quartic oscillators for initial pure and mixed states that are respectively taken to be the products and mixed density matrices of coherent states and squeezed states on each oscillator. The correlation with energy is also considered. It is shown that for the initial pure states with a small magnitude, two negativities are positively correlated with the von Neumann entropy while they are anti-correlated with the energy of each oscillator in the weak coupling regime. For mixed states with a small magnitude the two negativities and the mutual entropy exhibit dominantly positive correlation, whereas those three quantities are dominantly anti-correlated with the sum of energies of two oscillators in the case of weak interactions. Such correlation behaviors in the mixed state with small magnitudes are most striking at the same step in maximal and minimal values and in oscillation. The differences in entropies and negativities between coherent states and squeezed states are discussed. These are useful for quantum entanglement and quantum information processing.     

Maxwell's demon and the entropy cost of information

We present an analysis of Szilard's one-molecule Maxwell's demon, including a detailed entropy accounting, that suggests a general theory of the entropy cost of information. It is shown that the entropy of the demon increases during the expansion step, due to the decoupling of the molecule from the measurement information. It is also shown that there is an entropy symmetry between the measurement and erasure steps, whereby the two steps additivelv share a constant entropy change, but the proportion that occurs during each of the two steps is arbitrary. Therefore the measurement step may be accompanied by an entropy increase, a decrease, or no change at all, and likewise for the erasure step. Generalizing beyond the demon, decorrelation between a physical system and information about that system always causes an entropy increase in the joint system comprised of both the original system and the information. Decorrelation causes a net entropy increase in the universe unless, as in the Szilard demon, the information is used to decrease entropy elsewhere before the correlation is lost. Thus, information is thermodynamically costly precisely to the extent that it is not used to obtain work from the measured system.