Complementary relations in non-equilibrium stochastic processes.

We present novel complementary relations in non-equilibrium stochastic processes. Specifically, by utilising path integral formulation, we derive statistical measures (entropy, information, and work) and investigate their dependence on variables ( x , v ), reference frames, and time. In particular, we show that the equilibrium state maximises the simultaneous information quantified by the product of the Fisher information based on x and v while minimising the simultaneous disorder/uncertainty quantified by the sum of the entropy based on x and v as well as by the product of the variances of the PDFs of x and v . We also elucidate the difference between Eulerian and Lagrangian entropy. Our theory naturally leads to Hamilton–Jacobi relation for forced-dissipative systems. [ABSTRACT FROM AUTHOR]