Negative Thermophoretic Force in the Strong Coupling Regime

Abstract

Negative thermophoresis (a particle moving up the temperature gradient) is a somewhat counterintuitive phenomenon which has thus far eluded a simple thermostatistical description. The purpose of this letter is to show that a thermodynamic framework based on the formulation of a Hamiltonian of mean force has the descriptive ability to capture this interesting and elusive phenomenon in an unusually elegant and straightforward fashion. We propose a mechanism that describes the advent of a thermophoretic force acting from cold to hot on systems that are strongly coupled to a non-isothermal heat bath. When a system is strongly coupled to the heat bath, the system's eigenenergies Ej become effectively temperature-dependent. This adjustment of the energy levels allows the system to take heat from the environment, +d Ej , and return it as work, −d T dEj/dT. This effect can make the temperature-dependence of the effective energy profile non-monotonic. As a result, particles may experience a force in either direction depending on the temperature.

Strong Coupling and Nonextensive Thermodynamics

“…However, for systems with sufficiently low energy or sufficiently strong interactions, the system’s energy is comparable to the interaction energy, and the latter may no longer be neglected. Indeed, the presence of the interaction causes the effective Hamiltonian to be temperature-dependent, as long suggested by Elcock and Landsberg [ 16 ] and others [ 15 , 17 , 18 , 19 , 20 ].…”

“…The Hamiltonian of mean force is an extended Hamiltonian that accounts for interactions with the environment. It forms the basis of thermodynamics at strong coupling [ 12 , 13 , 14 ], a framework recently shown to provide a simple thermostatistical description of negative thermophoresis [ 15 ].…”

Internal geometric friction in a Kitaev-chain heat engine

“…Even before TDELs were proposed, the advantages of temperature-dependent mean potentials and corresponding forces were known in statistical mechanics of fluid mixtures [40]. A modern application of TDELs connects them to a temperature-dependent effective Hamiltonian, the so-called "Hamiltonian of mean force" to explore strong coupling of a small system to a heat bath [41,42], where counterintuitive negative thermophoresis effects can be explained using TDELs [43].…”

“…be found in the literature, due to dropping or partially keeping the partition functions [41][42][43]…”

Thermoelectric Conversion From Interface Thermophoresis and Piezoelectric Effects

“…Since the mover and stator of the thermophoretic system are bonded by vdW interactions, the dynamical properties of the thermophoretic mover are dependent not only on the thermal properties of the stator but also on the strength of the vdW interactions between the stator and mover. Recently, theoretical studies have shown that the vibration induced by the thermophoresis effect can be periodic and tuned by a temperature difference [38,40,43]. Therefore, the thermophoresis effect is a promising way to realize thermally induced piezoelectric conversion.…”