Hamiltonian mechanics is conservation of information entropy

In this work we show the equivalence between Hamiltonian mechanics and conservation of information entropy. We will show that distributions with coordinate independent values for information entropy require that the manifold on which the distribution is defined is charted by conjugate pairs (i.e.~it is a symplectic manifold). We will also show that further requiring that the information entropy is conserved during the evolution yields Hamilton's equations

Hamiltonian mechanics is conservation of information entropy

In this work we show the equivalence between Hamiltonian mechanics and conservation of information entropy. We will show that distributions with coordinate independent values for information entropy require that the manifold on which the distribution is defined is charted by conjugate pairs (i.e.~it is a symplectic manifold). We will also show that further requiring that the information entropy is conserved during the evolution yields Hamilton's equations

Risk analysis of complex hydrogen infrastructures

Developing a future sustainable refuelling station network is the next important step to establish hydrogen as a fuel for vehicles and related services. Such stations will most likely be integrated in existing refuelling stations and result in multi-fuel storages with a variety of fuels being delivered, stored and distributed, as e.g. biomass based methane, ethanol, gasoline, diesel as well as the traditional crude oil based products. Hydrogen is also in play as intermediate energy storage to secure the power supply based on large shares of fluctuating energy sources and as an intermediate to improve the quality of biomass based fuels. Therefore, hydrogen supply and distribution chains will likely not only serve to fulfil the demands of refuelling, but may also be important for the wider electrical power and fuel industries. Based on an integrated hydrogen supply and distribution network, the application of the method of “Functional modelling” is discussed in this paper to show the complexity of the coupling between power storage for electricity supply and supplying hydrogen for transportation. It will be shown how a “Functional model” can be applied for comprehensive data storage for various assessment methodologies, and how functional models could support coherent risk and sustainability (Risk Assessment, Life Cycle Assessment /Life Cycle Costing) assessments, in order to find optimal solutions for the development of the infrastructure on a regional or national level

The four postulates of quantum mechanics are three

The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this postulate contain some equivalent postulate or assumption (sometimes hidden). Here we give a natural definition of composite system as a set containing the component systems and show how one can logically derive the tensor product rule from the state postulate and from the measurement postulate. In other words, our paper reduces by one the number of postulates necessary to quantum mechanics.Comment: 4 pages+supplementary information. Final version accepted for publication on Phys. Rev. Let

The unphysicality of Hilbert spaces

We show that Hilbert spaces should not be considered the ``correct'' spaces to represent quantum states mathematically. We first prove that the requirements posited by complex inner product spaces are physically justified. We then show that completeness in the infinite-dimensional case requires the inclusion of states with infinite expectations, coordinate transformations that take finite expectations to infinite ones and vice-versa, and time evolutions that transform finite expectations to infinite ones in finite time. This makes Hilbert spaces physically unsound as they model a potential infinity as an actual infinity. We suspect that at least some problems in quantum theory related to infinities may be ultimately caused by the wrong space being used. We strongly believe a better solution can be found, and we look at Schwartz spaces for inspiration, as, among other things, they guarantee that the expectation of all polynomials of position and momentum are finite, guarantee solution to the moment problem and are the only space closed under Fourier transform.Comment: 5 pages plus mathematical appendi