Related papers: Unpredictability and basin entropy
Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…
The second law of nonequilibrium thermodynamics within the open system paradigm (a small system coupled to one or multiple baths) is derived. This is done by showing positivity of entropy production for arbitrary Hamiltonian dynamics for a…
In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…
This paper reports on a macroscopic fluctuation theory developed over the last ten years in collaboration with L. Bertini, A. De Sole, D. Gabrielli and C. Landim. This theory has been inspired by and tested on stochastic models of…
In order to better understand the occurrence of phase transitions, we adopt an approach based on the study of energy landscapes: The relation between stationary points of the potential energy landscape of a classical many-particle system…
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The…
The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is here extended to time dependent systems relaxing to equilibrium. We illustrate the main…
Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium…
We present the design and development of a data stream system that captures data uncertainty from data collection to query processing to final result generation. Our system focuses on data that is naturally modeled as continuous random…
Equilibrium statistical mechanics provides a robust framework for characterizing phase transitions in systems whose microsopic dynamics are time-reversible. Efforts to develop and validate theoretical frameworks for time-irreversible,…
We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system's state. This allows us to study directly entropy…
In the past several years, observational entropy has been developed as both a (time-dependent) quantum generalization of Boltzmann entropy, and as a rather general framework to encompass classical and quantum equilibrium and non-equilibrium…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
The past twenty years have seen a resurgence of interest in nonequilibrium thermodynamics, thanks to advances in the theory of stochastic processes and in their thermodynamic interpretation. Fluctuation theorems provide fundamental…
The question of the stability of unstable states of dynamical systems that do not explicitly contain a small parameter, chaos and bifurcations in them has attracted attention ever since [1-14]. This is due to the fact that this problem…
Multistability, the coexistence of multiple stable states, is a cornerstone of nonlinear dynamical systems, governing their equilibrium, tunability, and emergent complexity. Recently, the concept of hidden multistability, where certain…