Related papers: The entropy, from Clausius to functional inequalit…
In this paper, we consider a system of balance laws sufficiently general to contain the equations describing the thermomechanics of a one-dimensional continuum; this system involves some constitutive functions depending on the elements of…
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…
We extend the thermodynamic derivation of gravity in the Jacobson framework by generalizing the Clausius relation through a nontrivial entropy functional. We show that entropy deformations appear as modifications of the effective…
We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…
The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius'…
Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called ``caloric'') in transformations that are not isochoric (i.e.…
A new definition of entropy is introduced using a model that simulates an expanding space-time compatible with the fundamental principle of cosmology. The entropy is obtained by mean of a state function that measures the variation of the…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
The Markovian evolution of an open quantum system is characterized by a positive entropy production, while the global entropy gets redistributed between the system and the environment degrees of freedom. Starting from these premises, we…
The folding entropy is a quantity originally proposed by Ruelle in 1996 during the study of entropy production in the non-equilibrium statistical mechanics. As derived through a limiting process to the non-equilibrium steady state, the…
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…
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
When the difference between changes in energy and entropy at a given temperature is correlated with the ratio between the same changes in energy and entropy at zero average free energy of an ensemble of similar but distinct molecule-sized…
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in…
It is established that black holes have entropy and behave as thermodynamical systems. Associating entropy to gravitational fields has not remained limited to black holes, necessitating the notion of the second law of thermodynamics in…
The recursive property of entropy is well known in information theory; however, the concept is underutilized in thermodynamics, despite being the field where the concept of entropy originated. The zentropy approach is built on this idea,…
Conventional Non-equilibrium Thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper fluids will be considered in…
The entropy in dynamical systems was introduced by A. Kolmogorov. Initially dedicated to iterations of one finite measure preserving transformation, the notion was gradually generalized so as to encompass amenable group actions and…
A pair of symmetric expressions for the second law of thermodynamics is put forward. The conservation and transfer of entropy is discussed and applied to problems like biology, culture and life itself. A new explanation is given to the…