Related papers: Ergodic descriptors of nonergodic stochastic proce…
Modern biomedical, behavioral and psychological inference about cause-effect relationships respects an ergodic assumption, that is, that mean response of representative samples allow predictions about individual members of those samples.…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work,…
This paper analyzes the ergodic hypothesis in the context of Boltzmann's late work in statistical mechanics, where Boltzmann lays the foundations for what is today known as the typicality account. I argue that, based on the concepts of…
In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…
We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
Ergodicity breaking is a challenge for biological and psychological sciences. Ergodicity is a necessary condition for linear causal modeling. Long-range correlations and non-Gaussianity characterizing various biological and psychological…
Non-ergodicity impacts statistical inference in a diverse range of disciplines inside and outside of physics. However the concept of ergodicity is used inconsistently, and may refer to several nonequivalent notions. To help address this, we…