Entropy Production of a Harmonically Driven Order Parameter Field

Abstract

Ultrafast thermodynamics is an emerging field of research that aims to model the non-equilibrium dynamics of laser-excited materials. A central quantity of interest is the entropy production, which quantifies how far a system is from equilibrium. While previous theoretical works have modeled the entropy pro duction in terms of lattice vibrations and magnetization dynamics, this work models the entropy production of a scalar order parameter field coupled to a time-dependent harmonic driving field. In doing so, this thesis takes the first steps in bridging the gap between ultrafast thermodynamics and statistical field theory. The evolution of the field is modeled by the time-dependent Ginzburg-Landau equation, which is solved numerically. In the absence of a driving field, the va lidity of this method is confirmed through a finite-size scaling analysis in which equilibrium critical exponents are extracted and shown to agree with known val ues of the Ising/ϕ 4 universality class. An analytical expression for the entropy production is also proposed. This ex pression is compared with numerical simulations and, for a selected range of driving frequencies, exhibits clear quantitative agreement in the high-temperature phase. A finite-size scaling analysis of the entropy production further suggests that, for the driving protocol in question, the entropy production converges to a smooth function around the critical temperature, and as such does not exhibit any critical scaling.