Related papers: On the Mathematics of Information-Thermodynamics
We derive a formulation of the First Law of nonequilibrium thermodynamics for biological information-processing systems by partitioning entropy in the Second Law into microscopic and mesoscopic components and by assuming that natural…
We propose a computational method to measure the configurational entropy in generic polydisperse glass-formers. In particular, our method resolves issues related to the diverging mixing entropy term due to a continuous polydispersity. The…
Recently, some of us developed a novel model glass-forming liquid with k extra interactions with pseudo neighbours to each liquid particle over and above the regular interactions with its neighbours. Analysis of the structure and dynamics…
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…
We provide a unified thermodynamic formalism describing information transfers in autonomous as well as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is continuously generated in an auxiliary…
The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…
The maximum entropy method is shown to be a special limit of the stochastic analytic continuation method introduced by Sandvik [Phys. Rev. B 57, 10287 (1998)]. We employ a mapping between the analytic continuation problem and a system of…
In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the…
We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and…
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…
We set up a framework for quantum stochastic thermodynamics based solely on experimentally controllable, but otherwise arbitrary interventions at discrete times. Using standard assumptions about the system-bath dynamics and insights from…
Microcanonical equations for several thermodynamic properties of a system, suitable for molecular dynamics simulations, are derived from the nonextensive Tsallis entropy functional. Two possible definitions of temperature, the usual one and…
So far, feedback-driven systems have been discussed using (i) measurement and control, (ii) a tape interacting with a system or (iii) by identifying an implicit Maxwell demon in steady state transport. We derive the corresponding second…
We obtain macroscopic isothermal thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics in contact with a heat bath. The microscopic dynamics is given by a chain of anharmonic oscillators subject to a…
In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy-related quadratic tracer variances. Our approach relies on…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular sub-grid structure as many schemes do. IFD constructs an ensemble…
Symmetric alpha-stable (S alpha S) distributions with alpha<2 lack finite classical Fisher information. Building on Johnson's framework, we define Mixed Fractional Information (MFI) via the initial rate of relative entropy dissipation…