Related papers: Objective uncertainty relation with classical back…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
The characteristic function for the joint measurement of the changes of two commuting observables upon an external forcing of a quantum system is derived. In particular, the statistics of the internal energy, the exchanged heat and the work…
We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky-Margenau-Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
The transition from quantum to classical statistics is studied in light of Huggett's finding that the empirical data do not support the usual claim that the distinction between classical and quantum objects consists in the capacity of…
I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
We derive the uncertainty relation for a quantum open system comprised of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment…
The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
It is shown that the nature of quantum statistics can be clarified by assuming the existence of a background of random gravitational fields and waves, distributed isotropically in the space. This background is responsible for correlating…
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms…