Related papers: A probabilistic mechanics theory for random dynami…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory…
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicate details of the microscopic dynamics within a macroscopic system. The strength of Thermodynamics lies in…
Statistical mechanics descriptions of the second law of thermodynamics generally imply point-like particles driven by a dissipative overall mechanism for their simultaneous time-evolution. As the number of involved particles grows larger,…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
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…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
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…
We present here an exploration on on the physical implications of the Darwinian dynamics. We first show that how the nonequilibrium statistical mechanics emerges naturally. We then show that the first three laws of the thermodynamics, the…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumption that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to…
We examine the non-extensive approach to the statistical mechanics of Hamiltonian systems with $H=T+V$ where $T$ is the classical kinetic energy. Our analysis starts from the basics of the formalism by applying the standard variational…
The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from the risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular,…
The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy…