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)
Using dynamical concepts of phase transitions developed in earlier work, we exhibit the characteristic features of the spectrum and eigenfunctions to be expected when a hierarchy of phase transitions is present in a system, such as is expected to occur for spin glasses.
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)
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)
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)
We define and study a detailed many body model for the muscular contraction taking into account the various myosin heads. The state of the system is defined by the position of the actin and by an internal coordinate of rotation for each myosin head. We write a system of Fokker-Planck equations and calculate the average for the position, the number of… (More)
We continue, in this article, to develop the formalism of nonequilibrium thermodynamics in variational form. We prove that in the framework of progress variables, the Hamilton–Jacobi equation has always a simple solution, and we prove that this solution becomes a state function if and only if there is a thermodynamic equilibrium for the system. We study an… (More)
We consider reaction-diffusion systems that can be out of equilibrium. In the preceding article a path integral formation of the Hamilton–Jacobi approximation of the Master equation of such systems. Using this path integral formulation, it is possible to calculate rate constants for the transition from one well to another well of the information potential… (More)