Optimal Protocols and Optimal Transport in Stochastic Thermodynamics
Abstract
Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.
 Publication:

Physical Review Letters
 Pub Date:
 June 2011
 DOI:
 10.1103/PhysRevLett.106.250601
 arXiv:
 arXiv:1012.2037
 Bibcode:
 2011PhRvL.106y0601A
 Keywords:

 05.70.Ln;
 02.50.Ey;
 05.60.k;
 87.15.H;
 Nonequilibrium and irreversible thermodynamics;
 Stochastic processes;
 Transport processes;
 Dynamics of biomolecules;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 5 pages, RevTex41 format