Escape-rate theory

Ab Initio Derivation of Entropy Production Escape-Rate Theory... 

Proof with the Escape-Rate Theory Markov Chains and Information Theoretic Aspects Eluctuation Theorem for the Currents... 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

The spontaneous breaking of time-reversal symmetry also manifests itself in the escape-rate theory, which consists in putting the system out of equilibrium by... 

The formula (101) can also be proved with the escape-rate theory. We consider the escape of particles by difffusion from a large reservoir, as depicted in Fig. 17. The density of particles is uniform inside the reservoir and linear in the slab where diffusion takes place. The density decreases from the uniform value N/V of the reservoir down to zero at the exit where the particles escape. The width of the diffusive slab is equal to L so that the gradient is given by Vn = —N/ VL) and the particle current density J = —Wn = VN/ VL). Accordingly, the number of particles in the reservoir decreases at the rate... 

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