1,721,036 research outputs found
Steady-state probabilities for Markov jump processes in terms of powers of the transition rate matrix
Full text linkSeveral types of dynamics at stationarity can be described in terms of a Markov jump process among a finite number N of representative sites. Before dealing with the dynamical aspects, one basic problem consists in expressing the a priori steady-state occupation probabilities of the sites. In particular, one wishes to go beyond the mere black-box computational tools and find expressions in which the jump rate constants appear explicitly, therefore allowing for a potential design/control of the network. For strongly connected networks admitting a unique stationary state with all sites populated, here we express the occupation probabilities in terms of a formula that involves powers of the transition rate matrix up to order N - 1. We also provide an expression of the derivatives with respect to the jump rate constants, possibly useful in sensitivity analysis frameworks. Although we refer to dynamics in (bio)chemical networks at thermal equilibrium or under nonequilibrium steady-state conditions, the results are valid for any Markov jump process under the same assumptions
Probability inequalities for direct and inverse dynamical outputs in driven fluctuating systems
No full textWhen a fluctuating system is subjected to a time-dependent drive or nonconservative forces, the direct-inverse symmetry of the dynamics can be broken so inducing an average bias. Here we start from the fluctuation theorem, a cornerstone of stochastic thermodynamics, for inspecting the unbalancing between direct and inverse dynamical outputs, here called "events," in a bidirectional forward-backward setup. The occurrence of an event might correspond to the realization of a quantitative output, or to the realization of a sequence of acts that compose a complex "narrative." The focus is on mutual bounds between the probabilities of occurrence of direct and inverse events in the forward and backward mode. The inspection is made for systems in contact with a thermal bath, and by assuming Markov dynamics on the uncontrolled degrees of freedom. The approach comprises both the case of systems under a time-dependent drive and time-independent external forces. The general formulation is then used to derive (or re-derive) specialized results valid for finite-time processes, and for systems taken into steady conditions (either periodic steady states or steady states) starting from equilibrium. Among the results, we find already known forms of "generalized" thermodynamic uncertainty relations, and derive useful constraints concerning the work distribution function for systems in steady conditions
Stationary Markov jump processes in terms of average transition times: setup and some inequalities of kinetic and thermodynamic kind
No full textThe parametrization of continuous-time stationary Markov jump processes is worked out in terms of average times at which the site-to-site transitions take place again (recurrence) or occur starting from a given initial localization of the system (occurrence). The foremost result is the solution of the inverse problem of achieving the rate constants from an essential set of average occurrence/recurrence times. Then we provide the expression of the average entropy production rate at the stationary state in terms of average recurrence times only, elaborate the randomness parameter (squared coefficient of variation) which quantifies the relative precision of the timing of a given transition of interest, and derive some inequalities in which only a partial amount information about the network does enter. In particular, we get lower bounds on the randomness parameter and derive inequalities of both kinetic and thermodynamic kind
Upper bounding the average residence times in partially observed steady-state Markov jump processes
No full textSeveral types of stochastic dynamics can be modeled as a continuous-time Markov jump process among a finite number of sites. Within such framework, we face the problem of getting an upper bound on the average residence time of the system in a given site β (i.e., the average lifetime of the site) if what we can observe is only the permanence of the system in an adjacent site α and the occurrence of the transitions α→β. Supposing to have a long time record of this partial monitoring of the network under steady-state conditions, we show that an upper bound on the average time spent in the unobserved site can indeed be given. The bound is formally proved, tested by means of simulations, and illustrated for a multicyclic enzymatic reaction scheme
Steady-state solution of Markov jump processes in terms of arrival probabilities
No full textSeveral dynamical processes can be modeled as Markov jump processes among a finite number N of sites (the distinct physical states). Here we consider strongly connected networks with time-independent site-to-site jump rate constants, and focus on the steady-state occupation probabilities of the sites. We provide a physically framed expression of the steady-state distribution in terms of arrival probabilities, here defined as the probabilities of going from starting sites to target sites with a given number of jumps (regardless of the time required). In particular, the full set of return probabilities (for all the sites of the network) up to N-1 jumps is necessary and sufficient. A few examples illustrate the outcomes, including the case of stochastic chemical kinetics
Photoexcitation free energies of solvated molecules from raw absorption spectra: Can a Jarzynski-like equality be employed?
No full textA definition of photoexcitation free energy of solvated molecules, ΔAexc, is proposed by exploiting an analogy between optical transitions driven by the electromagnetic radiation and steered transformations in classical systems. We postulate the applicability of a ‘spectroscopic version’ of the Jarzynski equality (which was originally derived in the classical context) with a likely work distribution function obtainable from the experimental UV–vis spectrum, so to yield ΔAexc on empirical basis. Motivations that support such a postulate are provided, and tests of internal consistency are made on some model cases
Universal embedding of autonomous dynamical systems into a Lotka-Volterra-like format
Full text linkWe show that the ordinary differential equations (ODEs) of any deterministic autonomous dynamical system with continuous and bounded rate-field components can be embedded into a quadratic Lotka-Volterra-like form by turning to an augmented set of state variables. The key step consists in expressing the rate equations by employing the Universal Approximation procedure (borrowed from the machine learning context) with logistic sigmoid 'activation function'. Then, by applying already established methods, the resulting ODEs are first converted into a multivariate polynomial form (also known as generalized Lotka-Volterra), and finally into the quadratic structure. Although the final system of ODEs has a dimension virtually infinite, the feasibility of such a universal embedding opens to speculations and calls for an interpretation at the physical level
Dissipation, lag, and drift in driven fluctuating systems
No full textThis work deals with thermostated fluctuating systems subjected to driven transformations of the internal energetics. The main focus is on generally multidimensional systems with continuous configurational degrees
of freedom over which overdamped Markovian fluctuations take place (diffusive regime of the motion). Mutual bounds are established between the average energy dissipation, the deviation between nonequilibrium probability
density and underlying equilibrium distribution due to the system’s lag, and the statistical properties of the components of the directed flow induced by the transformation itself. The directed flow is here expressed in
terms of time-dependent “drift velocity” associated with the probability current in a advection-like formulation of the nonstationary Fokker-Planck equation. Consideration of the drift makes that the bounds achieved here
extend the inequality derived by Vaikuntanathan and Jarzynski [Europhys. Lett. 87, 60005 (2009)] involving only dissipation and lag. The key relations are then specified for the so-called stochastic pumps, i.e., systems
that reach a periodic steady state in response of cyclic transformations and that are prototypes of nonautonomous dissipative converters of input energy into directed motion; a one-dimensional case model is adopted to illustrate
the main features. Complementary results concerning bounds between the evolution rates of dissipation and lag, valid for both overdamped and underdamped dynamics, are also presented
Transverse Nuclear Spin Relaxation in Nematic Liquid Crystals. Angular Dependence of the Relaxation Rate in Pulsed Experiments
No full textThe theory underlying the slow-motional description of transverse relaxation in 2H-NMR pulsed experiments, sensitive to order director fluctuations in nematic liquid crystals, is outlined in a comprehensive way in order to highlight the physical parameters which enter the expressions elsewhere derived, to stress the limits of their applicability, and to address those experimental situations which may be more (or less) appealing from the point of view of the extent of information achievable from the analysis of the data. A comparison between fast-motional and slow-motional results is made here, for the first time, in relation to measures performed on samples aligned by the magnetic field
Shape dependence of the release rate of chemicals from plastic microparticles
Full text linkThe release of chemical additives from plastic microparticles in the aqueous phase represents a potential indirect threat for environment and biota. The estimate of the release timescale is demanded for drawing sensible conclusions on quantitative grounds. While the microparticles are generally taken to be spherical for ease of modelling, in reality the variety of shapes is large. Here, we face the problem of working out an empirical simple expression for estimating the release times for arbitrary shapes, assuming that the plastic material is in the rubbery state, that the dynamics inside the particle is a diffusion process, and that the release is irreversible. Our inspection is based on numerical simulations of the release process for randomly generated instances of regular and irregular geometries. The expression that we obtain allows one to estimate the release time in terms of the corresponding time (easy to compute) for the equal-volume spherical particle taken as reference, and of the ratio between the surface areas of particle and equivalent sphere
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