The Mesoscopic Dynamics of Thermodynamic Systems

Abstract

Concepts of everyday use such as energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and the general rules that the macroscopic properties of systems at equilibrium follow. Outside equilibrium and away from macroscopic regimes, most of those rules cannot be applied directly. Here we present recent developments that extend the applicability of thermodynamic concepts deep into mesoscopic and irreversible regimes. We show how the probabilistic interpretation of thermodynamics together with probability conservation laws can be used to obtain Fokker−Planck equations for the relevant degrees of freedom. This approach provides a systematic method to obtain the stochastic dynamics of a system directly from its equilibrium properties. A wide variety of situations can be studied in this way, including many that were thought to be out of reach of thermodynamic theories, such as nonlinear transport in the presence of potential barriers, activated processes, slow relaxation phenomena, and basic processes in biomolecules, such as translocation and stretching.

Concentration fluctuations in nonisothermal reaction-diffusion systems

“…͑13d͒ itself. In this respect we mention that, although this criticism may be valid, recent developments 17,18 have shown that by introducing an internal mesoscopic variable to describe the advancement of a chemical reaction, a linear phenomenological law similar to Eq. ͑13d͒ can be formulated in terms of that mesoscopic variable, thereby extending the validity of linear nonequilibrium thermodynamics ͑and its associated theory of fluctuating hydrodynamics, to be developed later in Sec.…”

Caveats of mean first-passage time methods applied to the crystallization transition: Effects of non-Markovianity

“…The main assumption of the MFPT and MLT methods is that the dynamics of the reaction in terms of the reaction coordinate, n s , is described by the onedimensional Fokker-Planck equation 14 for the probability density function p(n s , t) of n s at time t:…”

Multiscale Model for the Dielectric Permittivity

“…The relaxation of the polarisation can also be studied in the framework of nonequilibrium thermodynamics [5,7]. The relaxation process is dissipative and therefore entails an entropy production.…”