Random Interactions
Thermodynamics of bits and batteries
by Dr. Manoj Gopalkrishnan (TIFR)
Thursday, April 25, 2013
from
to
(Asia/Kolkata)
at Colaba Campus ( A304 )
at Colaba Campus ( A304 )
Description |
It is not uncommon in nonequilibrium statistical mechanics to describe a system by a Fokker-Planck equation obeying the fluctuation-dissipation theorem. If one treats the theory of such Fokker-Planck equations axiomatically, one finds that the finite models of this theory are precisely the detailed-balanced, finite Markov chains. In this setting, given a pair of systems each described by a Markov chain, we present an axiom that describes which detailed-balanced Markov chains on the product space are physically-valid interactions. To every system, we associate a real-valued function we call "internal action" on its probability simplex. This function captures not only how much free energy a system holds, but also how slowly this free energy relaxes to the equilibrium value. For triples consisting of two systems and an interaction between them, we conjecture an action processing inequality that interactions reduce internal action. Together with the Szilard-Landauer correspondence between energy and information, this implies the impossibility of spontaneous copying of information from a bit of low robustness to a bit of high robustness, i.e., a thermodynamic no-cloning. We are able to prove this conjecture for the simplest non-trivial case --- Markov chains with two states --- through case enumeration and explicit calculation. |