513 research outputs found
Maximal-entropy-production-rate nonlinear quantum dynamics compatible with second law, reciprocity, fluctuation-dissipation, and time-energy uncertainty relations
In view of the recent quest for well-behaved nonlinear extensions of the
traditional Schroedinger-von Neumann unitary dynamics that could provide
fundamental explanations of recent experimental evidence of loss of quantum
coherence at the microscopic level, in this paper, together with a review of
the general features of the nonlinear quantum (thermo)dynamics I proposed in a
series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)],
I show its exact equivalence with the maximal-entropy-production
variational-principle formulation recently derived in S.
Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on
the formalism of general interest I developed for the analysis of composite
systems, I show how the variational derivation can be extended to the case of a
composite system to obtain the general form of my equation of motion, that
turns out to be consistent with the demanding requirements of strong
separability. Moreover, I propose a new intriguing fundamental ansatz: that the
time evolution along the direction of steepest entropy ascent unfolds at the
fastest rate compatible with the time-energy Heisenberg uncertainty relation.
This ansatz provides a possible well-behaved general closure of the nonlinear
dynamics, compatible with the nontrivial requirements of strong separability,
and with no need of new physical constants. In any case, the time-energy
uncertainty relation provides lower bounds to the internal-relaxation-time
functionals and, therefore, upper bounds to the rate of entropy production.Comment: RevTeX; 19 pages; submitted to Phys.Rev.A on Feb.9, 2001; revised
version submitted on Sept.14, 2001 with slightly modified derivation in
Section III, improved discussion on strong separability in Sections X and IX,
added Eqs. 64b, 64c and 11
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
Recent Progress in the Definition of Thermodynamic Entropy
The principal methods for the definition of thermodynamic entropy are
discussed with special reference to those developed by Carath\'eodory, the
Keenan School, Lieb and Yngvason, and the present authors. An improvement of
the latter method is then presented. Seven basic axioms are employed: three
Postulates, which are considered as having a quite general validity, and four
Assumptions, which identify the domains of validity of the definitions of
energy (Assumption 1) and entropy (Assumptions 2, 3, 4). The domain of validity
of the present definition of entropy is not restricted to stable equilibrium
states. For collections of simple systems, it coincides with that of the proof
of existence and uniqueness of an entropy function which characterizes the
relation of adiabatic accessibility proposed by Lieb and Yngvason. However, our
treatment does not require the formation of scaled copies so that it applies
not only to collections of simple systems, but also to systems contained in
electric or magnetic fields and to small and few-particle systems.Comment: 23 pages, 5 figure
Rigorous and General Definition of Thermodynamic Entropy
The physical foundations of a variety of emerging technologies --- ranging
from the applications of quantum entanglement in quantum information to the
applications of nonequilibrium bulk and interface phenomena in microfluidics,
biology, materials science, energy engineering, etc. --- require understanding
thermodynamic entropy beyond the equilibrium realm of its traditional
definition. This paper presents a rigorous logical scheme that provides a
generalized definition of entropy free of the usual unnecessary assumptions
which constrain the theory to the equilibrium domain. The scheme is based on
carefully worded operative definitions for all the fundamental concepts
employed, including those of system, property, state, isolated system,
environment, process, separable system, system uncorrelated from its
environment, and parameters of a system. The treatment considers also systems
with movable internal walls and/or semipermeable walls, with chemical reactions
and/or external force fields, and with small numbers of particles. The
definition of reversible process is revised by introducing the new concept of
scenario. The definition of entropy involves neither the concept of heat nor
that of quasistatic process; it applies to both equilibrium and nonequilibrium
states. The role of correlations on the domain of definition and on the
additivity of energy and entropy is discussed: it is proved that energy is
defined and additive for all separable systems, while entropy is defined and
additive only for separable systems uncorrelated from their environment;
decorrelation entropy is defined. The definitions of energy and entropy are
extended rigorously to open systems. Finally, to complete the discussion, the
existence of the fundamental relation for stable equilibrium states is proved,
in our context, for both closed and open systems.Comment: 19 pages, RevTex
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