A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems

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On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion (2013, unknown): “Another interesting challenge is the stochastic origin of the gradient structure for general nonlinear reaction systems or even reaction-diffusion systems as discussed in [Mie11b].”
Weak–strong uniqueness of solutions to entropy-dissipating reaction–diffusion equations (2017, background): “It is also worth mentioning that reaction-diffusion equations with mass-action kinetics do not only dissipate the entropy (5), but may (formally and sometimes rigorously) be regarded as gradient flows of the entropy functional [27, 28, 29].”
An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow for the Entropy (2012, background): “A similar gradient flow structure in the space of probability measures has meanwhile been developed and exploited in many different settings [1, 2, 6, 9, 10, 12, 14, 15, 20, 22, 23, 25, 26].”
Gradient flow structures for discrete porous medium equations (2012, methodology): “Of course, if φ(r) = r, we recover the usual discrete heat equation associated with Q, which has been studied in [5, 11, 14].”