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Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in simple thermodynamic systems with temperature-independent heat capacities is TC/k. A…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…
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 thermal diffusion of a free particle is a random process and generates entropy at a rate equal to twice the particle temperature in natural units of information per second. The rate is calculated using a Gaussian process with a variance…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
A thermodynamic system of non-interacting quantum particles changes its statistical distribution formulas if there is a universal limitation for the size of energetic quantum leaps (magnitude of quantum leaps smaller than Planck energy). By…
We develop new modified cosmological scenarios by applying the first law of thermodynamics at the Universe horizon, utilizing a new entropic functional that generalizes the standard Boltzmann-Gibbs-Shannon entropy. In particular, starting…
We consider a class of autonomous Hamiltonian systems subject to small, time-periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation…
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
Entropy arises in strong interactions by a dynamical separation of ``partons'' from unobservable ``environment'' modes due to confinement. For interacting scalar fields we calculate the statistical entropy of the observable subsystem.…
Consistency constraints for low-energy theories, especially those lacking Lorentz invariance, have recently garnered attention. Building on results from black hole thermodynamics, we investigate the conjecture that leading irrelevant…
We test Boltzmann's H-theorem for several models of particle random walk. We study the influence of interaction between the particle and reservoir/detectors on entropy and find entropy increasing in time for some models and behaving…
The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…
An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagnetic field in the half Einstein universe. This geometry provides a mathematically convenient and physically instructive example of how the…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…
To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories, I show…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…