9,278 research outputs found
Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
In this paper we present a self-contained macroscopic description of
diffusive systems interacting with boundary reservoirs and under the action of
external fields. The approach is based on simple postulates which are suggested
by a wide class of microscopic stochastic models where they are satisfied. The
description however does not refer in any way to an underlying microscopic
dynamics: the only input required are transport coefficients as functions of
thermodynamic variables, which are experimentally accessible. The basic
postulates are local equilibrium which allows a hydrodynamic description of the
evolution, the Einstein relation among the transport coefficients, and a
variational principle defining the out of equilibrium free energy. Associated
to the variational principle there is a Hamilton-Jacobi equation satisfied by
the free energy, very useful for concrete calculations. Correlations over a
macroscopic scale are, in our scheme, a generic property of nonequilibrium
states. Correlation functions of any order can be calculated from the free
energy functional which is generically a non local functional of thermodynamic
variables. Special attention is given to the notion of equilibrium state from
the standpoint of nonequilibrium.Comment: 21 page
A derivation of a microscopic entropy and time irreversibility from the discreteness of time
All of the basic microsopic physical laws are time reversible. In contrast,
the second law of thermodynamics, which is a macroscopic physical
representation of the world, is able to describe irreversible processes in an
isolated system through the change of entropy S larger than 0. It is the
attempt of the present manuscript to bridge the microscopic physical world with
its macrosocpic one with an alternative approach than the statistical mechanics
theory of Gibbs and Boltzmann. It is proposed that time is discrete with
constant step size. Its consequence is the presence of time irreversibility at
the microscopic level if the present force is of complex nature (i.e. not
const). In order to compare this discrete time irreversible mechamics (for
simplicity a classical, single particle in a one dimensional space is selected)
with its classical Newton analog, time reversibility is reintroduced by scaling
the time steps for any given time step n by the variable sn leading to the
Nose-Hoover Lagrangian. The corresponding Nose-Hoover Hamiltonian comprises a
term Ndf *kB*T*ln(sn) (with kB the Boltzmann constant, T the temperature, and
Ndf the number of degrees of freedom) which is defined as the microscopic
entropy Sn at time point n multiplied by T. Upon ensemble averaging this
microscopic entropy Sn in equilibrium for a system which does not have fast
changing forces approximates its macroscopic counterpart known from
thermodynamics. The presented derivation with the resulting analogy between the
ensemble averaged microscopic entropy and its thermodynamic analog suggests
that the original description of the entropy by Boltzmann and Gibbs is just an
ensemble averaging of the time scaling variable sn which is in equilibrium
close to 1, but that the entropy term itself has its root not in statistical
mechanics but rather in the discreteness of time
Scan Quantum Mechanics: Quantum Inertia Stops Superposition
A novel interpretation of the quantum mechanical superposition is put
forward. Quantum systems scan all possible available states and switch randomly
and very rapidly among them. The longer they remain in a given state, the
larger the probability of the system to be found in that state during a
measurement. A crucial property that we postulate is quantum inertia, that
increases whenever a constituent is added, or the system is perturbed with all
kinds of interactions. Once the quantum inertia reaches a critical value
for an observable, the switching among the different eigenvalues of
that observable stops and the corresponding superposition comes to an end.
Consequently, increasing the mass, temperature, gravitational force, etc. of a
quantum system increases its quantum inertia until the superposition of states
disappears for all the observables and the system transmutes into a classical
one. The process could be reversible: decreasing the size, temperature,
gravitational force, etc. of a classical system one could revert the situation.
Entanglement can only occur between quantum systems, not between a quantum
system and a classical one, because an exact synchronization between the
switchings of the systems involved must be established in the first place and
classical systems do not have any switchings to start with. Future experiments
might determine the critical inertia corresponding to different
observables. In addition, our proposal implies a new radiation mechanism in
strong gravitational fields, giving rise to non-thermal synchrotron emission,
that could contribute to neutron star formation. Superconductivity,
superfluidity, Bose-Einstein condensates, and any other physical phenomena at
very low temperatures must be reanalyzed in the light of this interpretation,
as well as mesoscopic systems in general.Comment: 30 pages, no figures. Many improvements in the presentation,
including contents and a table, several references added. Ideas unchange
The role of the number of degrees of freedom and chaos in macroscopic irreversibility
This article aims at revisiting, with the aid of simple and neat numerical
examples, some of the basic features of macroscopic irreversibility, and, thus,
of the mechanical foundation of the second principle of thermodynamics as drawn
by Boltzmann. Emphasis will be put on the fact that, in systems characterized
by a very large number of degrees of freedom, irreversibility is already
manifest at a single-trajectory level for the vast majority of the
far-from-equilibrium initial conditions - a property often referred to as
typicality. We also discuss the importance of the interaction among the
microscopic constituents of the system and the irrelevance of chaos to
irreversibility, showing that the same irreversible behaviours can be observed
both in chaotic and non-chaotic systems.Comment: 21 pages, 6 figures, accepted for publication in Physica
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