Related papers: Maximum entropy change and least action principle …
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite…
The modern theory of rare events is grounded in near equilibrium ideas, however many systems of modern interest are sufficiently far from equilibrium that traditional approaches do not apply. Using the recently developed variational path…
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we…
We present a maximum entropy approach to analyze the internal dynamics of a small system in contact with a large bath e.g. a solute-solvent system. For the small solute, the fluctuations around the mean values of observables are not…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel…
The entropy maximum approach (Maxent) was developed as a minimization of the subjective uncertainty measured by the Boltzmann--Gibbs--Shannon entropy. Many new entropies have been invented in the second half of the 20th century. Now there…
In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…
The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a…
First we describe briefly an information-action method for the study of stochastic dynamics of hamiltonian systems perturbed by thermal noise and chaotic instability. It is shown that, for the ensemble of possible paths between two…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
This paper deals with temporal enzyme distribution in the activation of biochemical pathways. Pathway activation arises when production of a certain biomolecule is required due to changing environmental conditions. Under the premise that…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
Atypically large fluctuations in macroscopic non-equilibrium systems continue to attract interest. Their probability can often be determined by the optimal fluctuation method (OFM). The OFM brings about a conditional variational problem,…
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward…
When a system is driven out of equilibrium by a time-dependent protocol that modifies the Hamiltonian, it follows a nonequilibrium path. Samples of these paths can be used in nonequilibrium work theorems to estimate equilibrium quantities,…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…