4,264 research outputs found
Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics. Unified Implementation of the Maximum Entropy Production Principle
By suitable reformulations, we cast the mathematical frameworks of several
well-known different approaches to the description of non-equilibrium dynamics
into a unified formulation, which extends to such frameworks the concept of
Steepest Entropy Ascent (SEA) dynamics introduced by the present author in
previous works on quantum thermodynamics. The present formulation constitutes a
generalization also for the quantum thermodynamics framework. In the SEA
modeling principle a key role is played by the geometrical metric with respect
to which to measure the length of a trajectory in state space. In the near
equilibrium limit, the metric tensor is related to the Onsager's generalized
resistivity tensor. Therefore, through the identification of a suitable metric
field which generalizes the Onsager generalized resistance to the arbitrarily
far non-equilibrium domain, most of the existing theories of non-equilibrium
thermodynamics can be cast in such a way that the state exhibits a spontaneous
tendency to evolve in state space along the path of SEA compatible with the
conservation constraints and the boundary conditions. The resulting unified
family of SEA dynamical models is intrinsically and strongly consistent with
the second law of thermodynamics. Non-negativity of the entropy production is a
readily proved general feature of SEA dynamics. In several of the different
approaches to non-equilibrium description we consider here, the SEA concept has
not been investigated before. We believe it defines the precise meaning and the
domain of general validity of the so-called Maximum Entropy Production
Principle. It is hoped that the present unifying approach may prove useful in
providing a fresh basis for effective, thermodynamically consistent, numerical
models and theoretical treatments of irreversible conservative relaxation
towards equilibrium from far non-equilibrium states.Comment: 15 pages, 4 figures, to appear in Physical Review
Entropy and Entropy Production in Multiscale Dynamics
Heat conduction is investigated on three levels: equilibrium, Fourier, and
Cattaneo. The Fourier level is either the point of departure for investigating
the approach to equilibrium or the final stage in the investigation of the
approach from the Cattaneo level. Both investigations bring to the Fourier
level an entropy and a thermodynamics. In the absence of external and internal
influences preventing the approach to equilibrium the entropy that arises in
the latter investigation is the production of the classical entropy that arises
in the former investigation. If the approach to equilibrium is prevented, then
the entropy that arises in the investigation of the approach from the Cattaneo
level to the Fourier level still brings to the Fourier level the entropy and
the thermodynamics even if the classical entropy and the classical
thermodynamics is absent. We also note that vanishing total entropy production
as a characterization of equilibrium state is insufficient.Comment: Submitted to the Journal of Non-equilibrium Thermodynamic
Autonomous engines driven by active matter: Energetics and design principles
Because of its nonequilibrium character, active matter in a steady state can
drive engines that autonomously deliver work against a constant mechanical
force or torque. As a generic model for such an engine, we consider systems
that contain one or several active components and a single passive one that is
asymmetric in its geometrical shape or its interactions. Generally, one expects
that such an asymmetry leads to a persistent, directed current in the passive
component, which can be used for the extraction of work. We validate this
expectation for a minimal model consisting of an active and a passive particle
on a one-dimensional lattice. It leads us to identify thermodynamically
consistent measures for the efficiency of the conversion of isotropic activity
to directed work. For systems with continuous degrees of freedom, work cannot
be extracted using a one-dimensional geometry under quite general conditions.
In contrast, we put forward two-dimensional shapes of a movable passive
obstacle that are best suited for the extraction of work, which we compare with
analytical results for an idealised work-extraction mechanism. For a setting
with many noninteracting active particles, we use a mean-field approach to
calculate the power and the efficiency, which we validate by simulations.
Surprisingly, this approach reveals that the interaction with the passive
obstacle can mediate cooperativity between otherwise noninteracting active
particles, which enhances the extracted power per active particle
significantly.Comment: 21 pages, 8 figure
Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle
We present a mesoscopic model, based on the Boltzmann Equation, for the
interaction between a solid wall and a non-ideal fluid. We present an analytic
derivation of the contact angle in terms of the surface tension between the
liquid-gas, the liquid-solid and the gas-solid phases. We study the dependency
of the contact angle on the two free parameters of the model, which determine
the interaction between the fluid and the boundaries, i.e. the equivalent of
the wall density and of the wall-fluid potential in Molecular Dynamics studies.
We compare the analytical results obtained in the hydrodynamical limit for
the density profile and for the surface tension expression with the numerical
simulations. We compare also our two-phase approach with some exact results for
a pure hydrodynamical incompressible fluid based on Navier-Stokes equations
with boundary conditions made up of alternating slip and no-slip strips.
Finally, we show how to overcome some theoretical limitations connected with a
discretized Boltzmann scheme and we discuss the equivalence between the surface
tension defined in terms of the mechanical equilibrium and in terms of the
Maxwell construction.Comment: 29 pages, 12 figure
Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions
Previous and present "academic" research aiming at atomic scale understanding
is mainly concerned with the study of individual molecular processes possibly
underlying materials science applications. Appealing properties of an
individual process are then frequently discussed in terms of their direct
importance for the envisioned material function, or reciprocally, the function
of materials is somehow believed to be understandable by essentially one
prominent elementary process only. What is often overlooked in this approach is
that in macroscopic systems of technological relevance typically a large number
of distinct atomic scale processes take place. Which of them are decisive for
observable system properties and functions is then not only determined by the
detailed individual properties of each process alone, but in many, if not most
cases also the interplay of all processes, i.e. how they act together, plays a
crucial role. For a "predictive materials science modeling with microscopic
understanding", a description that treats the statistical interplay of a large
number of microscopically well-described elementary processes must therefore be
applied. Modern electronic structure theory methods such as DFT have become a
standard tool for the accurate description of individual molecular processes.
Here, we discuss the present status of emerging methodologies which attempt to
achieve a (hopefully seamless) match of DFT with concepts from statistical
mechanics or thermodynamics, in order to also address the interplay of the
various molecular processes. The new quality of, and the novel insights that
can be gained by, such techniques is illustrated by how they allow the
description of crystal surfaces in contact with realistic gas-phase
environments.Comment: 24 pages including 17 figures, related publications can be found at
http://www.fhi-berlin.mpg.de/th/paper.htm
Mesoscopic non-equilibrium thermodynamics approach to non-Debye dielectric relaxation
Mesoscopic non-equilibrium thermodynamics is used to formulate a model
describing non-homogeneous and non-Debye dielectric relaxation. The model is
presented in terms of a Fokker-Planck equation for the probability distribution
of non-interacting polar molecules in contact with a heat bath and in the
presence of an external time-dependent electric field. Memory effects are
introduced in the Fokker-Planck description through integral relations
containing memory kernels, which in turn are used to establish a connection
with fractional Fokker-Planck descriptions. The model is developed in terms of
the evolution equations for the first two moments of the distribution function.
These equations are solved by following a perturbative method from which the
expressions for the complex susceptibilities are obtained as a functions of the
frequency and the wave number. Different memory kernels are considered and used
to compare with experiments of dielectric relaxation in glassy systems. For the
case of Cole-Cole relaxation, we infer the distribution of relaxation times and
its relation with an effective distribution of dipolar moments that can be
attributed to different segmental motions of the polymer chains in a melt.Comment: 33 pages, 6 figure
Thermodynamic length in open quantum systems
The dissipation generated during a quasistatic thermodynamic process can be
characterised by introducing a metric on the space of Gibbs states, in such a
way that minimally-dissipating protocols correspond to geodesic trajectories.
Here, we show how to generalize this approach to open quantum systems by
finding the thermodynamic metric associated to a given Lindblad master
equation. The obtained metric can be understood as a perturbation over the
background geometry of equilibrium Gibbs states, which is induced by the
Kubo-Mori-Bogoliubov (KMB) inner product. We illustrate this construction on
two paradigmatic examples: an Ising chain and a two-level system interacting
with a bosonic bath with different spectral densities.Comment: 22 pages, 3 figures. v5: minor corrections, accepted in Quantu
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