asymptotics of work distributions in nonequilibrium systems the asymptotic behavior of the work distribution in driven nonequilibrium systems is determined using the method of optimal fluctuations for systems described by langevin dynamics the corresponding euler lagrange equation together with the appropriate boundary conditions and an equation for the leading pre exponential factor are derived the method is applied to three representative examples and the results are used to improve the accuracy of free energy estimates based on the application of the jarzynski equation

fluctuation theorems and atypical trajectories in this work we have studied simple models that can be solved analytically to illustrate various fluctuation theorems these fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work wc thermodynamic work w total entropy stot and dissipated heat q when the system is driven arbitrarily out of equilibrium all these quantities can be defined for individual trajectories we have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level as the time of observation increases the fraction of such atypical trajectories decreases as expected at the macroscale the distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak most probable value in the atypical regime without violating the expected average behaviour however dissipated heat and classical work exhibit a peak in the regime of typical behaviour only

superstatistical generalization of the work fluctuation theorem abstract we derive a generalized version of the work fluctuation theorem for non equilibrium systems with spatio temporal temperature fluctuations for 2 distributed inverse temperature we obtain a generalized fluctuation theorem based on q exponentials whereas for other temperature distributions more complicated formulae arise since q exponentials have a power law decay the decay rate in this generalized fluctuation theorem is much slower than the conventional exponential decay this implies that work fluctuations can be of relevance for the design of micro or nano structures since the work done on the system is relatively much larger than in the conventional fluctuation theorem

a new method for computing delay margins for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems we consider delay systems of retarded type modeled both as a high order scalar differential difference equation and as a set of first order differential difference equations expressed in state space form we provide a computational method that can be used to compute a delay interval such that the system under consideration is stable for all delay values that lie in the computed interval this method requires computing only the eigenvalues and generalized eigenvalues of certain constant matrices and it can be implemented efficiently based on this method we further state a simple necessary and sufficient condition concerning stability independent of delay for each of the two types of the models

critical delays and polynomial eigenvalue problems in this work we present a new method to compute the delays of delay differential equations ddes such that the dde has a purely imaginary eigenvalue for delay differential equations with multiple delays the critical curves or critical surfaces in delay space that is the set of delays where the dde has a purely imaginary eigenvalue are parameterized we show how the method is related to other works in the field by treating the case where the delays are integer multiples of some delay value i e commensurate delays the parameterization is done by solving a quadratic eigenvalue problem which is constructed from the vectorization of a matrix equation and hence typically of large size for commensurate delay differential equations the corresponding equation is a polynomial eigenvalue problem as a special case of the proposed method we find a closed form for a parameterization of the critical surface for the scalar case we provide several examples with visualizations where the computation is done with some exploitation of the structure of eigenvalue problems

lmi characterization of the strong delay independent stability of linear delay systems via quadratic lyapunov krasovskii functionals abstract in this note is proposed an analogue for linear delay systems of the characterization of asymptotic stability of the rational systems by the solvability of associated lyapunov equation it is shown that strong delay independent stability of delay system is equivalent to the feasibility of certain linear matrix inequality lmi related to quadratic lyapunov krasovskii functionals

stability and stabilization of delay differential systems the delay systems considered here are represented by linear delay differential equations the system parameters and the delays are assumed to be imperfectly known the instantaneous state vector is perturbed by a bounded external disturbance vector the problem addressed is that of characterizing conditions that guarantee that the trajectory of the instantaneous state vector remains in a domain defined by a set of symmetrical linear constraints it is shown that the positive invariance property can be used to solve this problem and that positive invariance of a compact domain of the instantaneous state space implies delay independent asymptotic stability of the associated deterministic system the possible use of these results for the control of a multiple delay mimo differential model is then presented finally an example is given

a minority game with bounded recall this paper studies a repeated minority game with public signals symmetric bounded recall and pure strategies we investigate both public and private equilibria of the game with fixed recall size we first show how public equilibria in such a repeated game can be represented as colored subgraphs of a de bruijn graph then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases we also show that private equilibria behave badly a private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff

asymptotic stability of neutral differential systems with many delays we are concerned with delay independent asymptotic stability of linear system of neutral differential equations we first establish a sufficient and necessary condition for the system to be delay independently asymptotically stable and then give some equivalent stability conditions this paper improves many recent results on the asymptotic stability in the literature one example is given to show that the sufficient and necessary condition is easy to verify

modulated two level system exact work statistics we consider an open two level system driven by a piecewise constant periodic field and described by a rate equation with fermi bose and arrhenius rates respectively we derive an analytical expression for the generating function and large deviation function of the work performed by the field and show that a work fluctuation theorem holds

work fluctuations in a time dependent harmonic potential rigorous results beyond the overdamped limit we investigate the stochastic motion of a brownian particle in the harmonic potential with a time dependent force constant it may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time dependent field we use the path integral formalism to solve the langevin equation and the associated fokker planck kramers equation rigorous relations are derived to generate the probability density function for the time dependent nonequilibrium work production beyond the overdamped limit we find that the work distribution exhibits an exponential tail with a power law prefactor accompanied by an interesting oscillatory feature multiple pseudo locking unlocking transitions due to the inertial effect some exactly solvable cases are discussed in the overdamped limit

quantum work fluctuation theorem exact case study for a perturbed oscillator we analytically explore the fluctuation of the work induced entropy production of an externally perturbed quantum harmonic oscillator interacting with several reservoirs the quantum fluctuation of the work amounts to a non gaussian fluctuation of the entropy production which interpolates the gaussian and the poissonian distributions at high and low temperature regimes also it is shown that the corresponding fluctuation theorem symmetry is rigorously satisfied

statistics of entropy production in linearized stochastic systems we consider a wide class of linear stochastic problems driven off the equilibrium by a multiplicative asymmetric force the force breaks detailed balance maintained otherwise thus producing entropy the large deviation function of the entropy production in the system is calculated explicitly the general result is illustrated using an example of a polymer immersed in a gradient flow and subject to thermal fluctuations

illustrative example of the relationship between dissipation and relative entropy kawai parrondo and van den broeck phys rev lett 98 080602 2007 have recently established a quantitative relationship between dissipated work and a microscopic information theoretic measure of irreversibility we illustrate this result using the exactly solvable system of a brownian particle in a dragged harmonic trap

empirical distributions of beliefs under imperfect observation let xn n be a process with values in a finite set x and law p and let yn f xn be a function of the process at stage n the conditional distribution pn p xnx1 xn1 element of x is the belief that a perfect observer who observes the process online holds on its realization at stage n a statistician observing the signals y1 yn holds a belief enp pnx1 xn on the possible predictions of the perfect observer given x and f we characterize the set of limits of expected empirical distributions of the process en when p ranges over all possible laws of xn n

fluctuation theorem uncertainty relation the fluctuation theorem is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations such as the second law of thermodynamics and the jarzynski equality recently the thermodynamic uncertainty relation was discovered which states that the fluctuation of observables is lower bounded by the entropy production in the present letter we derive a thermodynamic uncertainty relation from the fluctuation theorem we refer to the obtained relation as the fluctuation theorem uncertainty relation and it is valid for arbitrary dynamics stochastic as well as deterministic and for arbitrary antisymmetric observables for which a fluctuation theorem holds we apply the fluctuation theorem uncertainty relation to an overdamped langevin dynamics for an antisymmetric observable we demonstrate that the antisymmetric observable satisfies the fluctuation theorem uncertainty relation but does not satisfy the relation reported for current type observables in continuous time markov chains moreover we show that the fluctuation theorem uncertainty relation can handle systems controlled by time symmetric external protocols in which the lower bound is given by the work exerted on the systems

stability conditions for linear retarded functional differential equations abstract the purpose of this note is to study the exponential stability for the linear retarded functional differential equation x t 1 0 d x t r where the delay function r 0 is continuous and is of bounded variation on the interval 1 0 it is shown that the spectral limit function for the equation above has a continuous dependence on the pair r the set of all functions of bounded variation for which the equation above is exponentially stable for every delay function r the so called region of stability globally in the delays is a cone therefore for a fixed r the set of all which make our equation exponentially stable that is the region of stability for the delay function r contains a cone a discussion of the characterization of these regions of stability as well as of the largest cone contained in each region of stability for a fixed delay function r is given some remarks are made with respect to a similar question for the equation x t ax t 1 0 d x t r where a is a real n by n matrix is bounded variation on 1 0 and r as before several examples illustrate the results obtained

frequency sweeping tests for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems given in a state space form we consider specifically the notion of asymptotic stability independent of delay systems with both commensurate and noncommensurate delays are investigated we present for each class of systems a necessary and sufficient condition in terms of structured singular values and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work

exact results for the finite time thermodynamic uncertainty relation we obtain exact results for the recently discovered finite time thermodynamic uncertainty relation for the dissipated work w d in a stochastically driven system with non gaussian work statistics

explicit solution of the generalised langevin equation generating an initial condition for a langevin equation with memory is a non trivial issue we introduce a generalisation of the laplace transform as a useful tool for solving this problem in which a limit procedure may send the extension of memory effects to arbitrary times in the past this method allows us to compute average position work their variances and the entropy production rate of a particle dragged in a complex fluid by an harmonic potential which could represent the effect of moving optical tweezers for initial conditions in equilibrium we generalise the results by van zon and cohen finding the variance of the work for generic protocols of the trap in addition we study a particle dragged for a long time captured in an optical trap with constant velocity in a steady state our formulas open the door to thermodynamic uncertainty relations in systems with memory

on the complexity of coordination many results on repeated games played by finite automata rely on the complexity of the exact implementation of a coordinated play of length n for a large proportion of sequences this complexity appears to be no less than n we study the complexity of a coordinated play when allowing for a few mismatches we prove the existence of a constant c such that if m ln m n c for almost any sequence of length n there exists an automaton of size m that achieves a coordination ratio close to 1 with it moreover we show that one can take any constant c such that c e x ln x where x is the size of the alphabet from which the sequence is drawn our result contrasts with neyman 1997 that shows that when m ln m n is close to 0 for almost no sequence of length n there exists an automaton of size m that achieves a coordination ratio significantly larger 1 x with it

generalization of integral constraints on sensitivity to time delay systems extends results on integral constraints to time delay systems key technical issues in this extension include properties of nonminimum phase zeros the convergence of blaschke products and the poisson integral the results have implications for scalar and multivariable control system design as well as in filtering problems

non equilibrium thermodynamics and fluctuations abstract in the last 10 years a number of conventional fluctuation theorems have been derived for systems with deterministic or stochastic dynamics in a transient or in a non equilibrium stationary state these theorems gave explicit expressions for the ratio of the probability to find the system with a certain value of entropy or heat production to that of finding the opposite value a similar theorem for the fluctuations of the work done on a system has recently been demonstrated experimentally for a simple system in a transient state consisting of a brownian particle in water confined by a moving harmonic potential in this paper we show that because of the interaction between the stochastic motion of the particle in water and its deterministic motion in the potential very different new heat theorems are found than in the conventional case one of the consequences of these new heat fluctuation theorems is that the ratio of the probability for the brownian particle to absorb heat from rather than supply heat to the water is much larger than in the conventional fluctuation theorems this could be of relevance for micro nano technology

cooperation and effective computability a common interest game is a game in which there exists a unique pair of payoffs which strictly pareto dominates all other payoffs we consider the undiscounted repeated game obtained by the infinite repetition of such a two player stage game we show that if supergame strategies are restricted to be computable within church s thesis the only pair of payoffs which survives any computable tremble with sufficiently large support is the pareto efficient pair the result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future

vibrational control of linear time lag systems with arbitrarily large but bounded delays it is shown that vibrational stabilization can be effective for linear systems with large bounded delays theorems are given that define the procedures for the search of the stabilizing vibrations robust oscillatory stabilization insensitive to the delay size is also shown to take place for some classes of systems

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

power fluctuation theorem for a brownian oscillator in a thermal bath in this paper we prove the validity of the total power fluctuation theorem for a brownian particle in a harmonic trap when it is dragged out of equilibrium taking into account the inertia term in the langevin equation we first consider the theorem for an ordinary brownian harmonic oscillator embedded in a thermal bath as a second case we assume the presence of an electromagnetic field acting on the charged brownian oscillator in both cases the theorem is proved for two examples in the trap motion linear and oscillatory drag on the potential minimum

local kinetic interpretation of entropy production through reversed diffusion the time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time reversed drift and the noise prescription in the case of multiplicative noise the local kinematics and mechanics of free diffusion are linked to the hydrodynamic description these properties also provide an interpretation of the pope ching formula for the steady state probability density function along with a geometric interpretation of the fluctuation dissipation relation finally the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties and a stochastic differential equation for entropy production is obtained using the girsanov theorem for reversed diffusion the results are illustrated for the ornstein uhlenbeck process

finitely repeated games with finite automata the paper studies the implications of bounding the complexity of the strategies players may select on the set of equilibrium payoffs in repeated games the complexity of a strategy is measured by the size of the minimal automation that can implement it a finite automation has a finite number of states and an initial state it prescribes the action to be taken as a function of the current state and a transition function changing the state of the automaton as a function of its current state and the present actions of the other players the size of an automaton is its number of states the main results imply in particular that in two person repeated games the set of equilibrium payoffs of a sequence of such games g n n 1 2 converges as n goes to infinity to the individual rational and feasible payoffs of the one shot game whenever the bound on one of the two automata sizes is polynomial or subexponential in n and both the length of the game and the bounds of the automata sizes are at least n a special case of such result justifies cooperation in the finitely repeated prisoner s dilemma without departure from strict utility maximization or complete information but under the assumption that there are bounds possibly very large to the complexity of the strategies that the players may use

anomalous fluctuation properties we complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by l evy noise h touchette and e g d cohen phys rev e 76 020101 r 2007 as a concrete example we consider a particle subjected to a drag force and a l evy white noise with tail index ensuremath mu 0 2 and calculate the probability distribution of the work done on the particle by the drag force as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state for 0l ensuremath mu l2 both distributions satisfy what we call an anomalous fluctuation property characterized by positive and negative fluctuations that asymptotically have the same probability for ensuremath mu 2 by contrast the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations respectively which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations the difference between these different fluctuation behaviors is discussed in the context of large deviation theory experiments that could probe or reveal an anomalous fluctuation property are also discussed

on computing the maximal delay intervals for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems the authors consider delay systems of both retarded and neutral types expressed in state space forms the author s main goal is to provide a computation oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability the author s results show that this can be accomplished by computing the generalized eigenvalues of certain frequency dependent matrices based on these results the author also states a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems the author s results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units

absolute stability in linear delay differential systems ill posedness and robustness the author considers matrix delay differential systems which are polynomial in several delay operators using a necessary and sufficient criterion for stability independent of delay or absolute stability the author shows that system stability for all values of the delay vector lying in a sector will imply absolute stability we then show that absolute stability is ill posed with respect to arbitrarily small perturbations of the delay ratios if a certain extended delay differential system which is formed from the original is not also absolutely stable

imaginary characteristic roots of neutral systems with commensurate delays abstract this paper concentrates on stability analysis of neutral linear time invariant lti delay systems with multiple commensurate time delays a new numerical procedure is offered for the determination of purely imaginary characteristic roots of neutral delay systems which plays a crucial role in assessing the system stability based on simple linear algebra it is shown that the imaginary characteristic roots of such a system can be found by calculating the generalized eigenvalues of an associated matrix pair if the system is of retarded type we just need to determine the eigenvalues of a single matrix the results extend previously known work on neutral delay systems subject to a single delay for neutral systems subject to multiple commensurate delays in the light of the main result of this paper we present a new method to determine the largest first time delay interval for which a neutral delay system preserves its stability the paper is closed by showing numerical examples that illustrate the applicability and effectiveness of the proposed method

technical communique invariance properties in the root sensitivity of time delay systems with double imaginary roots if i w ir is an eigenvalue of a time delay system for the delay t 0 then i w is also an eigenvalue for the delays t k t 0 k2 p w for any k z we investigate the sensitivity periodicity and invariance properties of the root i w for the case that i w is a double eigenvalue for some t k it turns out that under natural conditions the condition that the root exhibits the completely regular splitting property if the delay is perturbed the presence of a double imaginary root i w for some delay t 0 implies that i w is a simple root for the other delays t k k 0 moreover we show how to characterize the root locus around i w the entire local root locus picture can be completely determined from the square root splitting of the double root we separate the general picture into two cases depending on the sign of a single scalar constant the imaginary part of the first coefficient in the square root expansion of the double eigenvalue

delay independent stability criteria for a class of retarded dynamical systems with two delays in this paper sufficient and necessary delay independent stability criteria are given for a class of retarded dynamical systems with two discrete time delays and parameters the delay independent stability problem of the system is discussed in terms of the stability of the characteristic function which is determined by checking the existence of real roots for some polynomials the criteria are also illustrated by examples

stationary and transient work fluctuation theorems for a dragged brownian particle recently wang et al carried out a laboratory experiment where a brownian particle was dragged through a fluid by a harmonic force with constant velocity of its center this experiment confirmed a theoretically predicted work related integrated transient fluctuation theorem itft which gives an expression for the ratio for the probability to find positive or negative values for the fluctuations of the total work done on the system in a given time in a transient state the corresponding integrated stationary state fluctuation theorem issft was not observed using an overdamped langevin equation and an arbitrary motion for the center of the harmonic force all quantities of interest for these theorems and the corresponding nonintegrated ones tft and ssft respectively are theoretically explicitly obtained in this paper while the tft and the itft are satisfied for all times the ssft and the issft only hold asymptotically in time suggestions for further experiments with arbitrary velocity of the harmonic force and in which also the issft could be observed are given in addition a nontrivial long time relation between the itft and the issft was discovered which could be observed experimentally especially in the case of a resonant circular motion of the center of the harmonic force

finite rationality and interpersonal complexity in repeated games a measure of complexity for repeated game strategies is studied this measure facilitates the investigation of some issues regarding finite rationality and the structure of subgame perfect equilibria of repeated games with discounting specifically the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set i e the number of distinct strategies induced by the original strategy in all possible subgames we observe that this cardinality is equal to the size cardinality of the state set of the smallest automaton which can implement the strategy thus in a sense complexity is measured on the basis of the amount of computing power inherent in the strategy a measure of strategic memory is also studied the following results are obtained 1 combining two notions of bounded rationality epsilon equilibrium and finite complexity we find that every subgame perfect equilibrium of the repeated game can be approximated with regard to payoffs by a subgame perfect epsilon equilibrium of finite complexity 2 for a generic class of normal form stage games at every discount robust subgame perfect drsp equilibrium there are necessary relationships among the complexities and memories of the players strategies in the two player case strategies must be equally complex and must have equal memories 3 for a second class of two pla yer stage games we show that the payoff vectors for all drsp equilibria are obtainable via equilibria in which the players strategies are equally complex and have equal memoiies

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

stability of linear neutral time delay systems exact conditions via matrix pencil solutions in this note we study the stability properties of linear neutral delay systems we consider systems described by both neutral differential difference and state space equations and we seek to determine the delay margin of such systems that is the largest range of delay values for which a neutral delay system may preserve its stability in both cases we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices which can be executed efficiently and with high precision the results extend previously known work on retarded systems and demonstrate that similar stability tests exist for neutral systems in particular the tests require essentially the same amount of computation required for retarded systems

zon cohen singularity and negative inverse temperature in a trapped particle limit we study a brownian particle on a moving periodic potential we focus on the statistical properties of the work done by the potential and the heat dissipated by the particle when the period and the depth of the potential are both large by using a boundary layer analysis we calculate a cumulant generating function and a biased distribution function the result allows us to understand a zon cohen singularity for an extended fluctuation theorem from a viewpoint of rare trajectories characterized by a negative inverse temperature of the biased distribution function

stability analysis for delay differential equations with multidelays and numerical examples in this paper we are concerned with the asymptotic stability of the delay differential equation x t a 0 x t a k x t k where a 0 a k c d d are constant complex matrices and x t k x 1 t k1 x 2 t k2 x d t kd t kl 0 stand for n x d constant delays k 1 n i 1 d we obtain two criteria for stability through the evaluation of a harmonic function on the boundary of a certain region we also get similar results for the neutral delay differential equation x t lx t m i x t i n j x t j where l m i and nj e c d d are constant complex matrices and i j 0 stands for constant delays i 1 m j 1 n numerical examples on various circumstances are shown to check our results which are more general than those already reported

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

optimal sign inverting control for time delayed systems a concept study with experiments an intriguing control logic sign inverting control sic is considered for control systems with delayed feedback it starts with a nominal control law formulated for non delayed case and simply inverts the sign of the control gains for some surprising benefits when used with the delays this operation sounds paradoxical as the sign inversion potentially harms the stability of the non delayed dynamics however sic with large delays may yield some complementary benefits to the nominal control logic from delay robustness perspective the main question we address in this paper is how to select the nominal control law so that such a contribution can be a feasible b optimal in some sense a structured methodology is proposed to achieve this starting with a linear quadratic regulator based controller a single scaling factor on the corresponding control gains is used for one dimensional optimisation experimental validation of the concept of this optimal sic procedure is also reported on a single axis

large deviations in the alternating mass harmonic chain we extend the work of kannan et al and derive the cumulant generating function cgf for the alternating mass harmonic chain consisting of n particles and driven by heat reservoirs the main result is a closed expression for the cgf in the thermodynamic large n limit this expression is independent of n but depends on whether the chain consists of an even or odd number of particles in accordance with the results obtained by kannan et al for the heat current this result is in accordance with the absence of local thermodynamic equilibrium in a linear system

polynomial two parameter eigenvalue problems and matrix pencil methods for stability of delay differential equations several recent methods used to analyze asymptotic stability of delay differential equations ddes involve determining the eigenvalues of a matrix a matrix pencil or a matrix polynomial constructed by kronecker products despite some similarities between the different types of these so called matrix pencil methods the general ideas used as well as the proofs differ considerably moreover the available theory hardly reveals the relations between the different methods in this work a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem the polynomial two parameter eigenvalue problem of which the quadratic two parameter eigenvalue problem is a special case this framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods we also recognize a few new matrix pencil variants to determine dde stability finally the recognition of the new types of eigenvalue problem opens a door to efficient computation of dde stability

large deviations for markov processes with resetting markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches foraging and population dynamics here we study the large deviations of time additive functions or observables of markov processes with resetting by deriving a renewal formula linking generating functions with and without resetting we are able to obtain the rate function of such observables characterizing the likelihood of their fluctuations in the long time limit we consider as an illustration the large deviations of the area of the ornstein uhlenbeck process with resetting other applications involving diffusions random walks and jump processes with resetting or catastrophes are discussed