# Increasing thermoelectric efficiency towards the Carnot limit

Basically their theory is that thermoelectric conversion of heat into electricity can reach the Carnot limit and have some new computational modeling to guide development toward that goal and to model materials in a way that would predict the figure of merit (how good they are at converting heat to electricity) for thermoelectrics which should speed up development.

They consider the cross transport of particles and energy in open classical ergodic
billiards. They show that, in the linear response regime, where they find exact expressions for all transport coefficients, the thermoelectric efficiency of ideal ergodic gases can approach Carnot efficiency for sufficiently complex charge carrier molecules. Their results are demonstrated with a simple numerical simulation of a Lorentz gas of particles with internal rotational degrees of freedom.

Large values of ZT , in principle approaching to Carnot’s efficiency, can be obtained when the energy of the carrier particles does not depend on the thermodynamic forces. The second law of thermodynamics only requires that L is
positive definite. Therefore, the second law does not impose any upper bound on the value of ZT . Furthermore, the crucial observation is that the Carnot’s limit
ZT = ∞ is reached when the energy density current and the electric current become proportional, since then det L = 0. ZT = ∞ follows from the fact that the average
particle’s energy hEi does not depend on the thermodynamic forces. In the context of classical physics this happens for instance in the limit of large number of internal degrees of freedom (d.o.f.), provided the dynamics is ergodic.

The suitability of a thermoelectric material for energy conversion or electronic refrigeration is evaluated by the thermoelectric figure of merit Z,
Z = σS2 / κ
where σ is the coefficient of electric conductivity, S is the Seebeck coefficient and κ is the thermal conductivity. The Seebeck coefficient S, also called thermopower, is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across the material.

Since the 1960’s many materials have been investigated but the maximum value found for ZT was achieved for the (Bi1−xSbx)2(Se1−yTey)3 alloy family with ZT ≈ 1. However,
values ZT > 3 are considered to be essential for thermoelectrics to compete in efficiency with mechanical power generation and refrigeration at room temperatures. The efforts recently focused on a bulk of new advanced thermoelectric materials and on low-dimensional materials, and only a small increment of the efficiency, ZT . 2.6, has been obtained.

They have performed the first numerical computation of ZT from deterministic microscopic equations of motion. Their method can be implemented for more realistic models where also quantum effects can be taken into account.