the simple exclusion process as seen from a tagged particle on considere le processus d exclusion simple comme ou a partir d une particule marquee on determine l ensemble des mesures invariantes et invariantes par translation sur z d

variations on the boman covering lemma abstract we explore some variants of the boman covering lemma and their relationship to the boundedness properties of the maximal operator let 1 p and let q be its conjugate exponent we prove that the strong type q q of the uncentered maximal operator by itself implies certain generalizations of the boman covering lemma for the exponent p and in turn these generalizations entail the weak type q q of the centered maximal operator we show by example that it is possible for the uncentered maximal operator to be unbounded for all 1 s while the conclusion of the lemma holds for every 1 p thus the latter condition is much weaker also the boundedness of the centered maximal operator entails weak versions of the lemma

stationary distributions of multi type totally asymmetric exclusion processes we consider totally asymmetric simple exclusion processes with n types of particle and holes n taseps on z and on the cycle z n angel recently gave an elegant construction of the stationary measures for the 2 tasep based on a pair of independent product measures we show that angel s construction can be interpreted in terms of the operation of a discrete time m m 1 queueing server the two product measures correspond to the arrival and service processes of the queue we extend this construction to represent the stationary measures of an n tasep in terms of a system of queues in tandem the proof of stationarity involves a system of n 1 taseps whose evolutions are coupled but whose distributions at any fixed time are independent using the queueing representation we give quantitative results for stationary probabilities of states of the n tasep on z n and simple proofs of various independence and regeneration properties for systems on z

random martingales and localization of maximal inequalities abstract let x d be a metric measure space for r 0 consider the hardy littlewood maximal operator m r f x def sup r r 1 b x r b x r f d we show that if there is an n 1 such that one has the microdoubling condition b x 1 1 n r b x r for all x x and r 0 then the weak 1 1 norm of m r has the following localization property m r l 1 x l 1 x sup r 0 m r r n r l 1 x l 1 x an immediate consequence is that if x d is ahlfors david n regular then the weak 1 1 norm of m r is n log n generalizing a result of stein and stromberg 1983 47 we show that this bound is sharp by constructing a metric measure space x d that is ahlfors david n regular for which the weak 1 1 norm of m 0 is n log n the localization property of m r is proved by assigning to each f l 1 x a distribution over random martingales for which the associated random doob maximal inequality controls the weak 1 1 inequality for m r

some inequalities for information divergence and related measures of discrimination inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics ergodic theory and other scientific fields we suggest new inequalities of this type often based on underlying identities as a consequence we obtain certain improvements of the well known pinsker inequality our study depends on two measures of discrimination called capacitory discrimination and triangular discrimination the discussion contains references to related research and comparison with other measures of discrimination e g ali silvey csiszar 1996 1966 divergences and in particular the hellinger distance

bounds on the concavity of quantum entropy we give new upper and lower bounds on the concavity of quantum entropy comparisons are given with other results in the literature

multiline queues with spectral parameters using the description of multiline queues as functions on words we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues we show that the spectral weight of a word is invariant under a natural action of the symmetric group giving a proof of the commutativity conjecture of arita ayyer mallick and prolhac we give a determinant formula for the spectral weight of a word which gives a proof of a conjecture of the first author and linusson

microscopic shape of shocks in a domain growth model considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities e g the inviscid burgers equation for the simple exclusion process the physical solutions of these partial differential equations develop discontinuities called shocks the microscopic structure of these shocks is of much interest and far from being well understood we introduce a domain growth model in which we find a stationary in time product measure for the model as seen from a defect tracer or second class particle traveling with the shock we also show that under some natural assumptions valid for a wider class of domain growth models no other model has stationary product measure as seen from the moving defect tracer

shock fluctuations in asymmetric simple exclusion the one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the burgers equation we study the process with rates of jumpsp q to the right and left respectively and with initial product measure with densities to the left and right of the origin respectively with shock initial conditions we prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times if this particle is added at another site then it describes the behavior of a characteristic of the burgers equation for vanishing left density 0 we prove in the scale t1 2 that the position of the shock at timet depends only on the initial configuration in a region depending ont the proofs are based on laws of large numbers for the second class particle

unified entropy trade off relations for a single quantum channel many important properties of quantum channels are quantified by means of entropic functionals characteristics of such a kind are closely related to different representations of a quantum channel in the jamiolkowski choi representation the given quantum channel is described by the so called dynamical matrix entropies of the rescaled dynamical matrix known as map entropies describe a degree of introduced decoherence within the so called natural representation the quantum channel is formally posed by another matrix obtained as the reshuffling of the dynamical matrix the corresponding entropies characterize an amount with which the receiver a priori knows the channel output as was previously shown the map and receiver entropies are mutually complementary characteristics indeed there exists a non trivial lower bound on their sum first we extend the concept of receiver entropy to the family of unified entropies developing the previous results we further derive non trivial lower bounds on the sum of the map and receiver q s entropies the derivation is essentially based on some inequalities with the schatten norms and anti norms

multipliers and singular integrals on exponential growth groups we propose a simple abstract version of calderon zygmund theory which is applicable to spaces with exponential volume growth and then show that important specific operators can be treated within this framework

dynamical entropy of c algebras and von neumann algebras the definition of the dynamical entropy is extended for automorphism groups ofc algebras as an example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density

shock fluctuations in the asymmetric simple exclusion process we consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively q p ferrari et al 1991 have shown that if the initial measure isv a product measure with densities and to the left and right of the origin respectively then there exists a microscopic shock for the system a shock is a random positionx t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively uniformly int we compute the diffusion coefficient of the shockd lim t t 1 e x t 2 ex t 2 and findd p q 1 1 1 as conjectured by spohn 1991 we show that in the scale sqrt t the position ofx t is determined by the initial distribution of particles in a region of length proportional tot we prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and this is the so called dynamical phase transition under shock initial conditions we show how the density fluctuation fields depend on the initial configuration

multiple shocks in bricklayers model in bricklayers model which is a generalization of the misanthrope processes we show that a nontrivial class of product distributions is closed under the time evolution of the process this class also includes measures fitting to shock data of the limiting pde in particular we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting in an attractive way via their jump rates our results are related to those of belitsky and schutz 4 on the simple exclusion process although we do not use quantum formalism as they do the structures we find are described from a fixed position similar ones were found in balazs 2 valak as seen from the random position of the second class particle

matrix representation of the stationary measure for the multispecies tasep in this work we construct the stationary measure of the n species totally asymmetric simple exclusion process in a matrix product formulation we make the connection between the matrix product formulation and the queueing theory picture of ferrari and martin in particular in the standard representation the matrices act on the space of queue lengths for n 2 the matrices in fact become tensor products of elements of quadratic algebras this enables us to give a purely algebraic proof of the stationary measure which we present for n 3

universal bounds for the holevo quantity coherent information and the jensen shannon divergence the mutual information between the sender of a classical message encoded in quantum carriers and a receiver is fundamentally limited by the holevo quantity using strong subadditivity of entropy we prove that the holevo quantity is not larger than an exchange entropy this implies an upper bound for coherent information moreover restricting our attention to classical information we bound the transmission distance between probability distributions by their entropic distance which is a concave function of their hellinger distance

the tasep speed process in the multi type totally asymmetric simple exclusion process tasep each site ofz is occupied by a labeled particle and two neighboring particles are int erchanged at rate one if their labels are in increasing order consider the process with the initial con figuration where each particle is labeled by its position it is known that in this case a s each particle has an asymptotic speed which is distributed uniformly on 1 1 we study the joint distribution of these speeds the tasep speed process we prove that the tasep speed process is a stationary measure for the multi type tasep dynamics consequently we can describe every ergodic stationary measure as a projection of the speed process measure this generalizes previous descriptions restricted to finitely many classes by combining this result with known stationary measures for taseps with finitely many types we compute several marginals of the speed process including the joint density of two and three consecutive speeds one striking property of the distribut ion is that two speeds are equal with positive probability and for any given particle there are infinitely m any others with the same speed we also study the partially asymmetric simple exclusion process asep we prove that the states of the asep with the above initial configuration seen as permutations ofz are symmetric in distribution this allows us to extend some of our results i ncluding the stationarity and description of all ergodic stationary measures also to the asep

exact solution of the totally asymmetric simple exclusion process shock profiles the microscopic structure of macroscopic shocks in the one dimensional totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles first and second class this nonequilibrium steady state factorizes about any second class particle which implies factorization in the one component system about the random shock position it also exhibits several other interesting features including long range correlations in the limit of zero density of the second class particles the solution also shows that a finite number of second class particles in a uniform background of first class particles form a weakly bound state

entropy of a subalgebra and quantum estimation in this paper we compare the accessible information of quantum communication channels with the entropic content of finite dimensional matrix algebras with respect to quantum states as defined by connes narnhofer and thirring in particular every abelian n n matrix algebra together with a density matrix define the input alphabet of a quantum communication channel whose accessible information equals the entropic content of the algebra with respect to the state the cases n 2 and n 3 are concretely examined in connection with the problem of the best estimation

singular integrals on symmetric spaces ii we extend some of our earlier results on boundedness of singular integrals on symmetric spaces of real rank one to arbitrary noncompact symmetric spaces our main theorem is a transference principle for operators defined by k bi invariant kernels with certain large scale cancellation properties as an application we prove l p boundedness of operators defined by fourier multipliers that satisfy singular differential inequalities of the hormandermichlin type

on the two species asymmetric exclusion process with semi permeable boundaries we investigate the structure of the nonequilibrium stationary state ness of a system of first and second class particles as well as vacancies holes on l sites of a one dimensional lattice in contact with first class particle reservoirs at the boundary sites these particles can enter at site 1 when it is vacant with rate and exit from site l with rate second class particles can neither enter nor leave the system so the boundaries are semi permeable the internal dynamics are described by the usual totally asymmetric exclusion process tasep with second class particles an exact solution of the ness was found by arita here we describe two consequences of the fact that the flux of second class particles is zero first there exist pinned and unpinned fat shocks which determine the general structure of the phase diagram and of the local measures the latter describe the microscopic structure of the system at different macroscopic points in the limit l in terms of superpositions of extremal measures of the infinite system second the distribution of second class particles is given by an equilibrium ensemble in fixed volume or equivalently but more simply by a pressure ensemble in which the pair potential between neighboring particles grows logarithmically with distance we also point out an unexpected feature in the microscopic structure of the ness for finite l if there are n second class particles in the system then the distribution of first class particles respectively holes on the first respectively last n sites is exchangeable

invariant measures for a two species asymmetric process we consider a process of two classes of particles jumping on a one dimensional lattice the marginal system of the first class of particles is the one dimensional totally asymmetric simple exclusion process when classes are disregarded the process is also the totally asymmetric simple exclusion process the existence of a unique invariant measure with product marginals with density and for the first and first plus second class particles respectively was shown by ferrari kipnis and saada recently derrida janowsky lebowitz and speer have computed this invariant measure for finite boxes and performed the infinite volume limit based on this computation we give a complete description of the measure and derive some of its properties in particular we show that the invariant measure for the simple exclusion process as seen from a second class particle with asymptotic densities and is equivalent to the product measure with densities to the left of the origin and to the right of the origin

random unistochastic matrices an ensemble of random unistochastic orthostochastic matrices is defined by taking squared moduli of elements of random unitary orthogonal matrices distributed according to the haar measure on u n or o n an ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble we study the distribution of complex eigenvalues of bistochastic unistochastic and orthostochastic matrices in the complex plane we compute averages entropy traces over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices

analogs of wiener s ergodic theorems for semisimple lie groups ii let g be a connected finite center simple lie group of real rank one and let k be a maximal compact subgroup of g let a at i t c r be a 1 parameter subgroup of hyperbolic translations such that g ka k is a cartan decomposition denote by ot the probability measure on g given by ot mk 6at mk where mk is the normalized haar measure on k let it denote the probablity measure with density vol bt 1xb g where bt g d gk k t and d denotes the canonical g invariant riemannian metric on g k let x b a be a standard borel probability space on which g acts measurably and ergodically by measure preserving transformations let 7r g iso lp x be the associated isometric representation and let 7r ut and 7r 3t denote the operators canonically associated with ct and it let n g dimr g k we prove maximal and pointwise ergodic theorems for the ball averages it on simple real rank one lie groups which are analogous to n wiener s maximal and pointwise ergodic theorems for ball averages on in the general case of ball averages on semisimple groups is completed in m n s our main result is the following

finitely correlated states on quantum spin chains we study a construction that yields a class of translation invariant states on quantum spin chains characterized by the property that the correlations across any bond can be modeled on a finite dimensional vector space these states can be considered as generalized valence bond states and they are dense in the set of all translation invariant states we develop a complete theory of the ergodic decomposition of such states including the decomposition into periodic neel ordered states the ergodic components have exponential decay of correlations all states considered can be obtained as local functions of states of a special kind so called purely generated states which are shown to be ground states for suitably chosen finite range vbs interactions we show that all these generalized vbs models have a spectral gap our theory does not require symmetry of the state with respect to a local gauge group in particular we illustrate our results with a one parameter family of examples which are not isotropic except for one special case this isotropic model coincides with the one dimensional antiferromagnet recently studied by affleck kennedy lieb and tasaki

on the equivalence between jensen shannon divergence and michelson contrast this paper focuses on the link between a visible linear and local distortion in a pictorial scene and its cost in terms of information theory quantities in particular a formal relation between the michelson visual contrast and the jensen shannon divergence jsd will be provided a universal just noticeable threshold is also derived by maximizing jsd constrained to the greatest michelson contrast of an invisible distortion such a threshold is independent of both distortion parameters and the probability density function of the degraded image it is then able to measure the bits budget to be spent for leaving the distortion invisible some tests on both synthetic and real distorted images validate the theoretical findings they confirm that the proposed universal threshold is really able to get the lower bound of human perception and then it may be useful for many applications such as bit allocation in coding procedures and automatic parameters setting in restoration algorithms

quantum cryptography without bell s theorem ekert has described a cryptographic scheme in which einstein podolsky rosen epr pairs of particles are used to generate identical random numbers in remote places while bell s theorem certifies that the particles have not been measured in transit by an eavesdropper we describe a related but simpler epr scheme and without invoking bell s theorem prove it secure against more general attacks including substitution of a fake epr source finally we show our scheme is equivalent to the original 1984 key distribution scheme of bennett and brassard which uses single particles instead of epr pairs

point set registration using havrda charvat tsallis entropy measures we introduce a labeled point set registration algorithm based on a family of novel information theoretic measures derived as a generalization of the well known shannon entropy this generalization known as the havrda charvat tsallis entropy permits a fine tuning between solution types of varying degrees of robustness of the divergence measure between multiple point sets a variant of the traditional free form deformation approach known as directly manipulated free form deformation is used to model the transformation of the registration solution we provide an overview of its open source implementation based on the insight toolkit of the national institutes of health characterization of the proposed framework includes comparison with other state of the art kernel based methods and demonstration of its utility for lung registration via labeled point set representation of lung anatomy

on the asymmetric simple exclusion process with multiple species in previous work the authors using the bethe ansatz found for the n particle asymmetric simple exclusion process on the integers a formula a sum of multiple integrals for the probability that a system is in a particular configuration at time t given an initial configuration the present work extends this to the case where particles are of different species with particles of a higher species having priority over those of a lower species here the integrands in the multiple integrals are defined by a system of relations whose consistency requires verifying that the yang baxter equations hold

recursive structures in the multispecies tasep we consider a multispecies generalization of the totally asymmetric simple exclusion process tasep with the simple hopping rule for the and th class particles the transition occurs with a rate independent from the values and ferrari and martin 2007 ann prob 35 807 obtained the stationary state of this model thanks to a combinatorial algorithm which was subsequently interpreted as a matrix product representation by evans et al 2009 j stat phys 135 217 this matrix ansatz shows that the stationary state of the multispecies tasep with n classes of particles n tasep can be constructed algebraically by the action of an operator on the n 1 tasep stationary state besides arita et al 2009 j phys a math theor 45 345002 analyzed the spectral structure of the markov matrix they showed that the set of eigenvalues of the n tasep contains those of the n 1 tasep and that the various spectral inclusions can be encoded in a hierarchical set theoretic structure known as the hasse diagram inspired by these works we define nontrivial operators that allow us to construct eigenvectors of the n tasep by lifting the eigenvectors of the n 1 tasep this goal is achieved by generalizing the matrix product representation and the ferrari martin algorithm in particular we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines markov matrices of different values of n

an estimate for a first order riesz operator on the affine group on the affine group of the line which is a solvable lie group of exponential growth we consider a right invariant laplacian a for a certain right invariant vector field x we prove that the first order riesz operator xa 1 2 is of weak type 1 1 with respect to the left haar measure of the group this operator is therefore also bounded on lp 1 p 2 locally the operator is a standard singular integral the main part of the proof therefore concerns the behaviour of the kernel of the operator at infinity and involves cancellation

on conjectures of classical and quantum correlations in bipartite states in this paper two conjectures which were proposed in luo et al 2010 phys rev a http dx doi org 10 1103 physreva 82 052122 on the correlations in a bipartite state ab are studied if the mutual information i ab between two quantum systems a and b before any measurement is considered as the total amount of correlations in the state ab then it can be separated into two parts classical correlations and quantum correlations the so called classical correlations c ab in the state ab are defined by the maximizing mutual information between two quantum systems a and b after von neumann measurements on system b we show that it is upper bounded by the von neumann entropies of both subsystems a and b which answered the conjecture on the classical correlation if the quantum correlations q ab in the state ab are defined by q ab i ab c ab we also show that it is upper bounded by the von neumann entropy of subsystem b it is also found that q ab is upper bounded by the von neumann entropy of subsystem a for a class of states

semigroup kernels on measures we present a family of positive definite kernels on measures characterized by the fact that the value of the kernel between two measures is a function of their sum these kernels can be used to derive kernels on structured objects such as images and texts by representing these objects as sets of components such as pixels or words or more generally as measures on the space of components several kernels studied in this work make use of common quantities defined on measures such as entropy or generalized variance to detect similarities given an a priori kernel on the space of components itself the approach is further extended by restating the previous results in a more efficient and flexible framework using the kernel trick finally a constructive approach to such positive definite kernels through an integral representation theorem is proved before presenting experimental results on a benchmark experiment of handwritten digits classification to illustrate the validity of the approach

statistical information and discrimination in analogy with the definition of shannon information m h de groot 1962 defined statistical information as the difference between prior and posterior risk of a statistical decision problem relations are studied between the statistical information and the discrimination functions of information theory known as f divergences using previous results it is shown that every f divergence i sub f p q is an average statistical information or decision problem with dichotomic parameter 0 1 loss function and corresponding observation distributions p and q the average is taken over a distribution on the parameter s prior probability this distribution is uniquely determined by the function f the main result is that every f divergence is statistical information in some properly chosen statistical decision problem and conversely that every piece of statistical information is an f divergence this provides a new representation of discrimination functions figuring in signal detection data compression coding pattern classification cluster analysis etc

quantum skew divergence in this paper we study the quantum generalisation of the skew divergence which is a dissimilarity measure between distributions introduced by lee in the context of natural language processing we provide an in depth study of the quantum skew divergence including its relation to other state distinguishability measures finally we present a number of important applications new continuity inequalities for the quantum jensen shannon divergence and the holevo information and a new and short proof of bravyi s small incremental mixing conjecture

on 1 qubit channels the entropy ht of a state with respect to a channel t and the holevo capacity of the channel require the solution of difficult variational problems for a class of 1 qubit channels which contains all the extremal ones the problem can be significantly simplified by attaching a unique hermitian antilinear operator to every channel of the considered class the channel s concurrence ct can be expressed by and turns out to be a flat roof this allows to write down an explicit expression for ht its maximum would give the holevo one shot capacity

bounds on information combining with quantum side information bounds on information combining are entropic inequalities that determine how the information entropy of a set of random variables can change when these are combined in certain prescribed ways such bounds play an important role in classical information theory particularly in coding and shannon theory entropy power inequalities are special instances of them the arguably most elementary kind of information combining is the addition of two binary random variables a cnot gate and the resulting quantities play an important role in belief propagation and polar coding we investigate this problem in the setting where quantum side information is available which has been recognized as a hard setting for entropy power inequalities our main technical result is a non trivial and close to optimal lower bound on the combined entropy which can be seen as an almost optimal quantum mrs gerber s lemma our proof uses three main ingredients 1 a new bound on the concavity of von neumann entropy which is tight in the regime of low pairwise state fidelities 2 the quantitative improvement of strong subadditivity due to fawzi renner in which we manage to handle the minimization over recovery maps and 3 recent duality results on classical quantum channels due to renes et al we furthermore present conjectures on the optimal lower and upper bounds under quantum side information supported by interesting analytical observations and strong numerical evidence we finally apply our bounds to polar coding for binary input classical quantum channels and show the following three results 1 even non stationary channels polarize under the polar transform 2 the blocklength required to approach the symmetric capacity scales at most sub exponentially in the gap to capacity and 3 under the aforementioned lower bound conjecture a blocklength polynomial in the gap suffices

open two species exclusion processes with integrable boundaries we give a complete classification of integrable markovian boundary conditions for the asymmetric simple exclusion process with two species or classes of particles some of these boundary conditions lead to non vanishing particle currents for each species we explain how the stationary state of all these models can be expressed in a matrix product form starting from two key components the zamolodchikov faddeev and ghoshal zamolodchikov relations this statement is illustrated by studying in detail a specific example for which the matrix ansatz involving 9 generators is explicitly constructed and physical observables such as currents densities calculated

a new metric for probability distributions we introduce a metric for probability distributions which is bounded information theoretically motivated and has a natural bayesian interpretation the square root of the well known spl chi sup 2 distance is an asymptotic approximation to it moreover it is a close relative of the capacitory discrimination and jensen shannon divergence

l1estimates for maximal functions and riesz transform on real rank 1 semisimple lie groups abstract let g be a real rank one semisimple lie group and k a maximal compact subgroup of g radial maximal operators for suitable dilations the heat and poisson maximal operators and the riesz transform which act on k bi invariant functions on g satisfy the l p norm inequalities for p 1 and a weak type l 1 estimate in this paper through the fourier theories on r and g we shall duplicate the hardy space h 1 r to a subspace h 1 s g s 0 of l 1 g and show that these operators are bounded from h 1 s g to l 1 g

on fractional maximal function and fractional integral on the laguerre hypergroup abstract let k 0 r be the laguerre hypergroup which is the fundamental manifold of the radial function space for the heisenberg group in this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional maximal operator and the fractional integral operator on the laguerre hypergroup from the spaces l p k to the spaces l q k and from the spaces l 1 k to the weak spaces w l q k

spherical maximal operator on symmetric spaces of constant curvature we prove an endpoint weak type maximal inequality for the spherical maximal operator applied to radial funcions on symmetric spaces of constant curvature and dimension n 2 more explicitly in the lorentz space associated with the natural isometry invariant measure we show that for every radial function f mf n c n f n 1 n the proof uses only geometric arguments and volume estimates and applies uniformly in every dimension

second class particles as microscopic characteristics in totally asymmetric nearest neighbor k exclusion processes summary we study aspects of the hydrodynamics of one dimensional totally asym metric k exclusion building on the hydrodynamic limit of seppalainen 1999 we prove that the weak solution chosen by the particle system is the unique one with maximal current past any fixed location a uniqueness result is needed because we can prove neither differentiability nor strict concavity of the flux function so we cannot use the lax oleinik formula or jump conditions to define entropy solutions next we prove laws of large numbers for a second class particle in k exclusion the macroscopic trajectories of second class particles are characteristics and shocks of the conservation law for the particle density in particular we extend tok exclusion ferrari s result that the second class particle follows a macroscopic shock in the rie mann solution the technical novelty of the proofs is a variational representation for the position of a second class particle in the context of the variational coupling method

jensen divergence based on fisher s information the measure of jensen fisher divergence between probability distributions is introduced and its theoretical grounds set up this quantity in contrast to the remaining jensen divergences grasps the fluctuations of the probability distributions because it is controlled by the local fisher information which is a gradient functional of the distribution so it is appropriate and informative when studying the similarity of distributions mainly for those having oscillatory character the new jensen fisher divergence shares with the jensen shannon divergence the following properties non negativity additivity when applied to an arbitrary number of probability densities symmetry under exchange of these densities vanishing under certain conditions and definiteness even when these densities present non common zeros moreover the jensen fisher divergence is shown to be expressed in terms of the relative fisher information as the jensen shannon divergence does in terms of the kullback leibler or relative shannon entropy finally the jensen shannon and jensen fisher divergences are compared for the following three large non trivial and qualitatively different families of probability distributions the sinusoidal generalized gamma like and rakhmanov hermite distributions which are closely related to the quantum mechanical probability densities of numerous physical systems

tight bounds for symmetric divergence measures and a refined bound for lossless source coding tight bounds for several symmetric divergence measures are derived in terms of the total variation distance it is shown that each of these bounds is attained by a pair of two or three element probability distributions an application of these bounds for lossless source coding is provided refining and improving a certain bound by csiszar another application of these bounds has been recently introduced by yardi et al for channel code detection

composition of quantum states and dynamical subadditivity we introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices this non abelian product is associative and stems from the composition of quantum maps acting on a simple quantum system it induces a semi group in the subset of states with maximally mixed partial traces subadditivity of the von neumann entropy with respect to this product is proved it is equivalent to subadditivity of the entropy of bistochastic maps with respect to their composition where the entropy of a map is the entropy of the corresponding state under the jamiolkowski isomorphism strong dynamical subadditivity of a concatenation of three bistochastic maps is established analogous bounds for the entropy of a composition are derived for general stochastic maps in the classical case they lead to new bounds for the entropy of a product of two stochastic matrices