Abstract
The multi-dimensional non-linear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to non-linear transform of variables. The formalism involves no metric or affine connection, works for systems with or without detailed balance, and is substantially simpler than previous theories. Its relation with deterministic theory is clarified. The unitary limit and Hermitian limit of the theory are examined. Some implications on the choices of stochastic calculus are also discussed.
Highlights
Nonlinear Langevin theory with multiplicative noises [1,2,3,4] is widely used to describe dynamics out of equilibrium
While earlier works mostly focus on processes with detailed balance (DB), more recently there have been many efforts trying to develop nonlinear Langevin dynamics lacking DB [27,28,29,30,31,32,33]
Equations (3.9), (3.11), and (3.14) demonstrate the physical significance of the tilde process defined by LFP: It is the macroscopic time reversal of original process corresponding to LFP, because all macroscopic properties are reversed
Summary
Nonlinear Langevin theory with multiplicative noises [1,2,3,4] is widely used to describe dynamics out of equilibrium. There have been extensive and long-lasting discussions on the choice of stochastic calculus [5,6,7,8,9,10], relation between deterministic and stochastic description [11,12,13], as well as the covariance of theory under nonlinear transform of variables (NTV) [15,16,17,18]. We discuss a covariant formulation of nonlinear Langevin theory which involves no metric tensor or affine connection. V, we conclude this work with some comments on the general issue of stochastic calculus
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
