Related papers: H-theorem do-conjecture
Quantum mechanics manifests in experimental observations in several ways. Hauge et al. (1987) and Leavens et al. (1989) had pointed out that interference effects dominate a physical quantity called injectance. We show that, very…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
Non-traditional thermodynamics, applied to random behaviour associated with turbulence, mixing and competition, is reviewed and analysed. Competitive mixing represents a general framework for the study of generic properties of competitive…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
A heuristic generalization of the Boltzmann-Gibbs microcanonical entropy is proposed, able to describe meta-equilibrium features and evolution of macroscopic systems. Despite its simple-minded derivation, such a function of "collective…
Collective intelligence emerges across biological, physical, and artificial systems without central coordination, yet a unifying principle governing such behaviour remains elusive. The Free Energy Principle explains how individual agents…
The Fluctuation Theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy…
In many cases the Nash equilibria are not predictive of the experimental players' behaviour. For some games of Game Theory it is proposed here a method to estimate the probabilities with which the different options will be actually chosen…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
A system of spins coupled to a bath is a traditional setup in open quantum systems. Through Heisenberg's equation, the spin dynamics can be modeled by a set of first-order differential equations. Interpreting the terms as colored noise and…
A single mechanism, endemic to the standard model of physics, is proposed to explain wavefunction collapse, classical motion, dissipation, equilibration, and the transition from pure quantum mechanics through open system decoherence to the…
Modern physics is founded on two mainstays: mathematical modelling and empirical verification. These two assumptions are prerequisite for the objectivity of scientific discourse. Here we show, however, that they are contradictory, leading…
One observes that a considerable level of confusion remains about some of those aspects of irreversibility, entropy generation and `the arrow of time' which actually are well understood. This demands that great care must be taken in any…
Boltzmann's H-Theorem, formulated 150 years ago in terms of H-function that also bears his name, is one of the most celebrated theorems of science and paved the way for the development of nonequilibrium statistical mechanics. Nevertheless,…
The classical Second Law of Thermodynamics demands that an isolated system evolves with a non-diminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum…
The dissipative dynamics anticipated in the proof of 't Hooft's existence theorem -- "For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization" -- is constructed here…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…