Related papers: Is Entropy Associated with Time's Arrow?
We derive a generalization of the Second Law of Thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
The development of stochastic thermodynamics during the last decades prompted the discovery of novel nonequilibrium relations refining our understanding of the second law in small fluctuating systems and its connection with information…
It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…
Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several…
Within the general formalism of quantum theory irreversibility and the arrow of time in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of entropy production. This motivates…
This study introduces the syntropy function ($S_N$) and expectancy function ($E_N$), derived from the novel function $\phi$, to provide a refined perspective on complexity, extending beyond conventional entropy analysis. $S_N$ is designed…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence $S(x)$. We establish recurrence…
A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is given both in the finite and…
We take the view that the standard von Neumann definition, in which the entropy $S^{vN}$ of a pure state is zero, is in evident conflict with the statement of the second law that the entropy of the universe $S_{univ}$ increases in…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
We share a small connection between information theory, algebra, and topology - namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their…
Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity…
The second law of thermodynamics states that for a thermally isolated system entropy never decreases. Most physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger…
This paper argues that the common identification of time with entropy is a category error. Entropy accounts for the arrow of time but not for time itself. Even in a maximally entropic universe the so called heat death temporal structure…
An essential role of information in microscopic thermodynamics (e.g. Maxwell's demon) opens a challenging question if there exists a formulation of the second law of thermodynamics based only on pure information ideas. Here, such a…
Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the…
In the scientific and engineering literature, the second law of thermodynamics is expressed in terms of the behavior of entropy in reversible and irreversible processes. According to the prevailing statistical mechanics interpretation the…
A hypothesis proposed in the paper (Entropy 2017, 19, 345) on the deductive formulation of a physical theory based on explicitly- and universally-introduced basic concepts is further developed. An entropic measure of time with a number of…