Negative Thermophoretic Force in the Strong Coupling Regime

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 nonisothermal heat bath. When a system is strongly coupled to the heat bath, the system's eigenenergies E_{j} become effectively temperature dependent. This adjustment of the energy levels allows the system to take heat from the environment, +d⟨E_{j}⟩, and return it as work, -d⟨TdE_{j}/dT⟩. This effect can make the temperature dependence of the effective energy profile nonmonotonic. As a result, particles may experience a force in either direction depending on the temperature.