Bernard Gaveau

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In this work, we consider the nonequilibrium thermodynamics of a reaction-diffusion system at a given temperature, using the Master equation. The information potential is defined as the logarithm of the stationary state. We compare the approximations, given by the Fokker–Planck equation and the Wentzel-Kramers-Brillouin method directly applied to the Master(More)
The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical because 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(More)
We propose a novel definition of efficiency, valid for motors in a nonequilibrium stationary state exchanging heat and possibly other resources with an arbitrary number of reservoirs. This definition, based on a rational estimation of all irreversible effects associated with power production, is adapted to the concerns of sustainable development. Under(More)
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 multidimensional 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(More)
In this article, we define stochastic dynamics for a system coupled to reservoirs. The rules for forward and backward transitions are related by a generalized detailed balance identity involving the system and its reservoirs. We compare the variation of information and of entropy. We define the Carnot dissipation and prove that it can be expressed in terms(More)
The Grusin operator ∆G = 1 2 (∂ 2 x + x 2 ∂ 2 y), x, y ∈ R, is studied by Hamilton-Jacobi theory. In particular, we find all the geodesics of ∆G of the induced nonholonomic geometry, construct a modified complex action f which allows us to obtain the heat kernel Pt of ∆G. The small time asymptotics of Pt at all critical points of f are computed. Finally we(More)
In this paper, we prove a general inequality for the macroscopic relaxation towards a stationary nonequilib-rium state. Namely, the rate of dissipation of energy in the system always exceeds the rate of dissipation of information ͑up to temperature͒. Here the information function is defined as the logarithm of the stationary probability distribution divided(More)