Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Dynamical chemistry: non-equilibrium effective actions for reactive fluids

Journal Article · · Journal of Statistical Mechanics

Abstract We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved—or to account for chemical reactions, non-conserved—currents to local-equilibrium parameters. The second method involves a higher-brow approach in which we attack the same problem from the perspective of non-equilibrium effective field theory (EFT). Non-equilibrium effective actions are defined using the in–in formalism on the Schwinger–Keldysh contour and are therefore capable of describing thermal fluctuations and dissipation as well as quantum effects. The non-equilibrium EFT approach is especially powerful as all terms in the action are fully specified by the symmetries of the system; in particular the second law of thermodynamics does not need to be included by hand, but is instead derived from the action itself. We find that the equations of motion generated by both methods agree, but the EFT approach yields certain advantages. To demonstrate some of these advantages we construct a quadratic action that is valid to very small distance scales—much smaller than the scales at which ordinary hydrodynamic theories break down. Such an action captures the full thermodynamic and quantum behavior of reactions and diffusion at quadratic order. Finally, taking the low-frequency and low-wavenumber limit, we reproduce the linearized version of the well-known reaction–diffusion equations as a final coherence check.

Research Organization:
Columbia Univ., New York, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0011941
OSTI ID:
1979426
Journal Information:
Journal of Statistical Mechanics, Vol. 2022, Issue 7; ISSN 1742-5468
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English

References (9)

More on gapped Goldstones at finite density: more gapped Goldstones journal November 2013
Effective field theory of dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current journal September 2017
Effective field theory of dissipative fluids journal September 2017
Global anomalies, discrete symmetries and hydrodynamic effective actions journal January 2019
A quantum hydrodynamical description for scrambling and many-body chaos journal October 2018
On thermal fluctuations and the generating functional in relativistic hydrodynamics journal July 2015
Constraints on fluid dynamics from equilibrium partition functions journal September 2012
Phenomenological Lagrangians journal April 1979
Path-integral formula for local thermal equilibrium journal August 2017