Nonlinear Dynamics and Chaos, Non-equilibrium Physics

Classical Speed Limits

We are currently focused on developing a classical density theory that draws remarkable parallels with the density matrix formulation of quantum mechanics. Our theory is designed to ensure norm-preserving evolutiion in the tangent space of deterministic systems and is applicable to both Hamiltonian and dissipative dynamics.

Figure 1

Figure 1: How quickly can the growth rate of a local perturbation to a system change over time? [Das & Green, PRR (Letter), 2023]

One major finding of this theory is that it has allowed us to obtain first time-information uncertainty relations for deterministic systems, including those that are relevant to Lyapunov exponents and phase space dissipation rate. This theory also leads to the maximum speed on thermodynamic entropy production with deep connections with deterministic fluctuation theorems.

Figure 2

Figure 2: What is the minimum entropy production rate that can occur in a given time interval? [Das & Green, PRE (Letter), 2024]

An interesting new element that has emerged from this work is a classical Fisher information specifically tailored for deterministic differentiable dynamics analogous to quantum Fisher information. This information measure directly connects the phase space geometry with the instability of a dynamical system.