相关论文: Anholonomic Transformations of Mechanical Action P…
Based only on classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike recent identities between…
We present and discuss a selected set of problems of classical mechanics and thermodynamics. The discussion is based on the use of the impulse-momentum equation simultaneously with the centre-of-mass (pseudo-work) equation or with the first…
Mobile microscopic bodies, such as motile cells, can be modelled phenomenologically as ``active particles'' which can move against external forces by depleting an internal energy depot. The microscopic mechanisms underlying such ``active''…
This paper aims to investigate the thermodynamic formalism of weighted amenable topological pressure for factor maps of amenable group actions. Following the approach of Tsukamoto [\emph{Ergodic Theory Dynam. Syst.} \textbf{43}(2023),…
We propose a new form of nonrelativistic quantum mechanics which is based on a quantum version of the action principle.
The dynamics of anisotropic particles are dictated by forces and torques that can be challenging to mathematically represent in computer simulations. Several data-driven approaches have been developed to approximate these interactions, but…
We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
We introduce the concept of action space, a set $\boldsymbol{X}$ endowed with an action cost $\mathsf{a}:(0,+\infty)\times \boldsymbol{X}\times \boldsymbol{X}\to [0,+\infty)$ satisfying suitable axioms, which turn out to provide a `dynamic'…
Magnetic textures can be manipulated by electric currents via the mechanisms of spin-transfer and spin-orbit-torques. We review how these torques can be exploited to create chiral magnetic textures in magnets with broken inversion…
The homogeneous causal action principle on a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed. The Euler-Lagrange equations are derived…
We prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such operators in dimension $n$ and $3$-forms in dimension $n + 1$.…
The paper aims to apply the octonions to explore the precessional angular velocities of several particles in the electromagnetic and gravitational fields. Some scholars utilize the octonions to research the electromagnetic and gravitational…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
We obtain macroscopic adiabatic thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics subject to random collisions with the environment. The microscopic dynamics is given by a chain of oscillators…
In this paper our main aim is to develop some basic properties of hyperbolic valued metric spaces. We also establish the hyperbolic version of Banach contraction principle. Further we construct a hyperbolic valued metric on the space of all…
By applying Schwinger's variational principle to the Einstein$-$Cartan action for the gravitational field, we derive quantum commutation relations between the metric and torsion tensors.
The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when…
A modification of the Adaptive Biasing Force method is introduced, in which the free energy is approximated by a sum of tensor products of one-dimensional functions. This enables to handle a larger number of reaction coordinates than the…