Activated kinetics in a nonequilibrium thermal bath

Abstract

Changing rates of activated transitions with changing temperature is at the heart of the theory of chemical reactions. It is commonly expressed by the Arrhenius law, which asserts that reactions overcoming a potential (activation) barrier slow down as temperature is lowered. The reason is that each activated event occurs by drawing, by a random fluctuation, the kinetic energy from the surrounding heat bath to overcome the barrier of the potential energy. The probability of such a fluctuation decreases with cooling, thus slowing the kinetics down. In this established paradigm, temperature is a thermodynamic equilibrium parameter, constant across the sample, something that is only controlled by adding or subtracting heat from the entire macroscopic vessel in which the experiment is performed. In PNAS, Craven and Nitzan (1) explore what happens if this standard picture is modified to allow different parts of the reacting system, the reactants and products, to possess different temperatures.How can temperature be different between reactants and products? From the macroscopic perspective, any heat flow should be associated with a temperature gradient; the two quantities are connected by the Kapitza thermal resistance (2). Therefore, any reaction with the thermal heat flow between the reactants and products will produce a temperature gradient between them. This is the configuration that Craven and Nitzan (1) put forward by considering the reactants and products at their corresponding temperatures T R and T P (Fig. 1). In contrast to the standard formulation of nonequilibrium thermodynamics, where only the chemically reacting subsystem is far from the equilibrium and the bath (which is the source or sink of thermal energy) is fully equilibrated (3), one arrives at the picture of chemical reactions occurring in a nonequilibrium thermal bath.To establish the transport of heat between molecules involved in chemical reactions, the length of the temperature change needs to scale down to nanometers (nanoscale) (2). In addition to practical difficulties of achieving this setup, one faces the challenging fundamental question of how to define temperature at such a small length scale. Temperature is well-defined in equilibrium thermodynamics of macroscopic materials, but the definitions of "nonequilibrium temperature" (4) and "local temperature" (5) differ between the applications and in general are not universal. The notion of a fictive temperature is often invoked in glass science, where it quantifies the amount of potential energy of a system trapped in a nonequilibrium state in excess to its equilibrium potential energy (6, 7). In this terminology, any activated event involves raising the system's fictive temperature to the level consistent with the top of the activation barrier. In equilibrium systems, this occurs by spontaneous fluctuations (8), but the state of high fictive temperature can be alternatively achieved by either fast quenching of a hot system to a lower temperature or by bringing either reactants or products ...

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

“…However, its often discussed identification with the Arrhenius activation energy turns out to be transparent only in particular cases [22][23][24][25], specifically in temperature ranges where it is a constant or varies slowly. (b) The reciprocal temperature dependence of the reciprocal activation energy…”

“…The Tolman expression for E a , as the difference between the average energy of chemically successful collisions and the total kinetic energy of the gas where the reaction occurs, attributes to this quantity the meaning of an energetic requirement for the reaction to occur. However, its often discussed identification with the Arrhenius activation energy turns out to be transparent only in particular cases [22][23][24][25], specifically in temperature ranges where it is a constant or varies slowly.…”

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle

“…The most common case is a process driven by two thermal sources (N = 2), and this system has been the focus of intensive investigation due to its relevance for vibrational heat conduction 7,10-20 and electron-transfer-induced heat transport. [21][22][23][24]50 In this article, the general derivations of the restricted properties are valid for arbitrary N. For simplicity, the results shown in all figures are for the N = 2 model.…”

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. II. Heat transfer and energy partitioning of a free particle

“…While ∆E = 0 for an unrestricted ensemble at steady state, in this paper we investigate this quantity in the restricted case where ∆E can be nonzero. A process driven by two thermal sources (N = 2) is the most common case due to its relevance for heat transport in molecular systems, 12,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]61 and all numerical results in this article are for this scenario. The time-dependence of the heat obtained-by/released-into the system from baths 1 and 2 for a system driven by two sources is shown in Fig.…”