Related papers: Generalized Entropy approach to far-from-equilibri…
The Macroscopic Fluctuating Theory is presented from a practical and self consistent point of view. We take as starting point the assumption that a system at a mesoscopic scale is described by a field $\phi(x,t)$ that evolves by a Langevin…
We establish a novel generalization of the fluctuation theorem for partially-masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
Within the Tsallis thermodynamics' framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be…
We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We…
Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…
The macroscopic fluctuation theory is a powerful tool to characterise the large scale dynamical properties of diffusive systems, both in- and out-of-equilibrium. It relies on an action formalism in which, at large scales, the dynamics is…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom,…
This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production…
Starting from the geometrical interpretation of the R\'enyi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle…
Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns…
New formulations of quantum generalized fluctuation-dissipation relations in terms of characteristic and probabilistic functionals of continuous observations are suggested and discussed. It is shown that control of entropy production in…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We study the long-time asymptotics for the so-called McKendrick-Von Foerster or renewal equation, a simple model frequently considered in structured population dynamics. In contrast to previous works, we can admit a bounded measure as…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
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…
Fluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature and velocity), in…
We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial…