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For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation…

A general quantum theory encompassing Mechanics, Thermodynamics and irreversible dynamics is presented in two parts. The first part is concerned exclusively with the description of the states of any individual physical system. It is based…

Rolling of a small sphere on a solid support is governed by a non-linear friction that is akin to the Coulombic dry fiction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention…

Any quantum theory of gravity which treats the gravitational constant as a dynamical variable has to address the issue of superpositions of states corresponding to different eigenvalues. We show how the unobservability of such…

We discuss inertial effects in systems outside equilibrium within the framework of non-equilibrium thermodynamics. By introducing a Gibbs equation in which the entropy depends on the probability density, we are able to describe a system of…

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches…

We study the resonances of the quantum kicked rotor subjected to an excitation that follows an aperiodic Fibonacci prescription. In such a case the secondary resonances show a sub-ballistic behaviour like the quantum walk with the same…

We introduce a type of quantum dissipation -- local quantum friction -- by adding to the Hamiltonian a local potential that breaks time-reversal invariance so as to cool the system. Unlike the Kossakowski-Lindblad master equation, local…

The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in…

The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…

We study the properties of the one-dimensional Fibonacci chain, subjected to the placement of on-site impurities. The resulting disruption of quasiperiodicity can be classified in terms of the renormalization path of the site at which the…

We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction…

Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude…

Let us imagine that there is an overall quantum theory (not necessarily recognized yet) of matter and energy ({\it i.e.}, of elementary fermions and bosons) interacting with the physical spacetime (treated on a quantum level). Since states…

We consider a proposed alternative to quantum gravity, in which the spacetime metric is treated as classical, even while matter fields remain quantum. Consistency of the theory necessarily requires that the metric evolve stochastically.…

Anderson's nonstandard construction of brownian motion as an infinitesimal random walk on the euclidean line is generalized to an Hausdorff riemannian manifold. A nonstandard Feynman-Kac formula holding on such an Hausdorff riemannian…

The cosmological constant problem is principally concerned with trying to understand how the zero-point energy of quantum fields contributes to gravity. Here we take the approach that by addressing a fundamental unresolved issue in quantum…

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of…