Related papers: Entropy, heat, and G\"odel incompleteness
Examples of irreversible thermodynamic theory of nonlocal phenomena are given, based on generalized entropy current. Thermodynamic currents and forces are identified to derive the Guyer-Krumhansl and Cahn-Hilliard equations. In the latter…
It is a widespread belief that results like G\"odel's incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity's strive for scientific knowledge. As the argument goes, there are…
In classical thermodynamics, irreversible processes are accomplished with an increase of entropy and a release of heat into the environment. In the case of black hole thermodynamics, instead, the increase of entropy is related with the…
We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of…
1. Strong and weak notions of erasure are distinguished according to whether the single erasure procedure does or does not leave the environment in the same state independently of the pre-erasure state. 2. Purely thermodynamic…
The entropy production in dissipative processes is the essence of the arrow of time and the second law of thermodynamics. For dissipation of quantum systems, it was recently shown that the entropy production contains indeed two…
Entanglement entropy is often speculated as a strong candidate for the origin of the black-hole entropy. To judge whether this speculation is true or not, it is effective to investigate the whole structure of thermodynamics obtained from…
The Schwarzschild's black hole dynamics in presence of gravity is described on using the thermodynamic equations of state for contractile materials. Its entropy and temperature, obtained by using classical principles, reproduce the results…
After a discussion on the state of local equilibrium with temperature inhomogeneity, comparing mixture state reprsentation in statistical mechanics and pure state representation in thermo field dynamics, a simple model is solved to show…
The need for improved functionalities is driving the search for more complicated multi-component materials. Despite the factorially increasing composition space, ordered compounds with 4 or more species are rare. Here, we unveil the…
Identical classical particles are distinguishable. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and from the relation S = k ln W leads to a non-extensive expression for the entropy.…
Macroscopic many-body systems always exhibit irreversible behaviors together with the entropy increase. However, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville…
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.…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
On the basis of the entropy of incomplete statistics (IS) and the joint probability factorization condition, two controversial problems existing in IS are investigated, where one is what the correct expression of the internal energy for a…
Various quantum thermodynamic bounds are shown to stem from a single tighter and more general inequality, consequence of the operator concavity of the logarithmic function. Such an inequality, which we call the "thermodynamic reverse…
A nonequilibrium system is characterized by a set of thermodynamic forces and fluxes which give rise to entropy production (EP). We show that these forces and fluxes have an information-geometric structure, which allows us to decompose EP…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being…