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B. Gaveau

Publications and source records attributed to B. Gaveau.

12 recordsLinked to original sources
arXiv2014

Relative entropy, interaction energy and the nature of dissipation

Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. By calculating a transport coefficient we show that indeed---at least in this case---the source of dissipation in that coefficient is the relative entropy.

cond-mat.stat-mech↗
arXiv2013

Dissipation, interaction and relative entropy

Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients.

cond-mat.stat-mech↗
arXiv2011

Efficiency of a thermodynamic motor at maximum power

Several recent theories address the efficiency of a macroscopic thermodynamic motor at maximum power and question the so-called "Curzon-Ahlborn (CA) efficiency." Considering the entropy exchanges and productions in an n-sources motor, we study the maximization of its power and show that the controversies are partly due to some imprecision in the maximization variables. When power is maximized with respect to the system temperatures, these temperatures are proportional to the square root of the corresponding source temperatures, which leads to the CA formula for a bi-thermal motor. On the other hand, when power is maximized with respect to the transitions durations, the Carnot efficiency of a bi-thermal motor admits the CA efficiency as a lower bound, which is attained if the duration of the adiabatic transitions can be neglected. Additionally, we compute the energetic efficiency, or "sustainable efficiency," which can be defined for n sources, and we show that it has no other universal upper bound than 1, but that in certain situations, favorable for power production, it does not exceed 1/2.

cond-mat.stat-mech↗
arXiv2011

Violation of the zeroth law of thermodynamics for a non-ergodic interaction

The phenomenon described by our title should surprise no one. What may be surprising though is how easy it is to produce a quantum system with this feature; moreover, that system is one that is often used for the purpose of showing how systems equilibrate. The violation can be variously manifested. In our detailed example, bringing a detuned 2-level system into contact with a monochromatic reservoir does not cause it to relax to the reservoir temperature; rather, the system acquires the reservoir's level-occupation-ratio.

cond-mat.stat-mech↗
arXiv2008

Generalized Clausius relation and power dissipation in non equilibrium stochastic systems

We extend certain basic and general concepts of thermodynamics to discrete Markov systems exchanging work and heat with reservoirs. In this framework we show that the celebrated Clausius inequality can be generalized and becomes an equality, significantly extending several recent results. We further show that achieving zero dissipation in a system implies that detailed balance obtains, and as a consequence there is zero power production. We obtain inequalities for power production under more general circumstances and show that near equilibrium obtaining maximum power production requires dissipation to be of the same order of magnitude.

cond-mat.stat-mech↗
arXiv2006

Ratcheting up energy by means of measurement

The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical since the destroyed correlations are ordinarily considered negligible. Mathematically the explanation is straightforward and physically one can identify the degrees of freedom supplying this energy. Nevertheless, the energy input can be calculated without specific reference to those degrees of freedom.

quant-ph↗
arXiv2006

Multiple phases in stochastic dynamics: geometry and probabilities

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an \textit{observable-representation of state space}, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state.

cond-mat.stat-mech↗
arXiv2001

Slow relaxation, confinement, and solitons

Millisecond crystal relaxation has been used to explain anomalous decay in doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons. Our model exhibits confinement of mechanical energy released by excitation. Extending the model to long times is justified by its relation to solitons, excitations previously proposed to occur in alkali halides. Soliton damping and observation are also discussed.

cond-mat.mtrl-sci↗
arXiv2001

Coarse grains: the emergence of space and order

The emergence of macroscopic variables can be effected through {\it coarse graining}. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced in the coarse graining, we do not provide a unique prescription. Most significantly, the grains, and by implication entropy, are only defined modulo a characteristic time scale of observation.

cond-mat.stat-mech↗