Related papers: Entropy is complexity
Thermodynamics is usually developed starting from entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example in the context of local…
For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…
Based on Landauer's principle, we provide a geometrical definition for the entropy of a given static, spherically symmetric spacetime. Considering a congruence of geodesics across a surface, one defines the entropy of a congruence as the…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
We have presented first an axiomatic derivation of Boltzmann entropy on the basis of two axioms consistent with two basic properties of thermodynamic entropy. We have then studied the relationship between Boltzmann entropy and information…
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…
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as…
From a new rigorous formulation of the general axiomatic foundations of thermodynamics we derive an operational definition of entropy that responds to the emergent need in many technological frameworks to understand and deploy thermodynamic…
We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second…
The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws…
For an isolated assembly that comprises a system and its surrounding reservoirs, the total entropy ($S_{a}$) always monotonically increases as time elapses. This phenomenon is known as the second law of thermodynamics ($S_{a}\geq0$). Here…
Statistical mechanics descriptions of the second law of thermodynamics generally imply point-like particles driven by a dissipative overall mechanism for their simultaneous time-evolution. As the number of involved particles grows larger,…
The Kelvin-Planck statement of the Second Law of Thermodynamics is a stricture on the nature of heat receipt by any body suffering a cyclic process. It makes no mention of temperature or of entropy. Beginning with a Kelvin-Planck statement…
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the…
In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
We investigate the validity of the generalized second law of thermodynamics, in the cosmological scenario where dark energy interacts with both dark matter and radiation. Calculating separately the entropy variation for each fluid component…
We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the…
The R\'enyi entropy is a mathematical generalization of the concept of entropy and it encodes the total information of a system as a funtion of its order parameter $\alpha$. The meaning of the R\'enyi entropy in physics is not completely…