Title: Speed limits on the dynamics of complex systems
Speaker: Dr. Swetamber Das, Department of Physics, University of Massachusetts, Boston
Abstract: Predicting the dynamical behavior of complex systems poses a fundamental challenge in describing diverse phenomena, from planetary orbit stability to the thermodynamics of protein folding. In this context, a key consideration is the limitation imposed by the timescales involved in the evolution. For quantum mechanical systems, the Heisenberg’s uncertainty principle quantifies this limitation, while for classical systems, particularly those exhibiting chaos, the Lyapunov time provides a characteristic timescale. This prompts us to ask: are there bounds on timescales for deterministic systems evolving in phase space? In this talk, I will explore this question and show, in particular, that the time evolution of local Lyapunov exponents and the dissipation rate of phase space volume adhere to a set of fundamental bounds which we can express as speed limits. The mathematical forms of our classical speed limits [1–3] bear striking similarities to the well-known quantum speed limits. To obtain these classical speed limits we develop and use a density matrix framework [4, 5] that offers an alternative computationally tractable basis for the statistical mechanics of non-equilibrium systems. These speed limits apply to a wide range of complex systems, whether they are isolated, dissipative, or driven.
[1] Swetamber Das and Jason R. Green. Speed limits on deterministic chaos and dissipation. Phys. Rev. Res. (Letter), 5:L012016 (2023).
[2] Mohamed Sahbani, Swetamber Das, and Jason R. Green. Classical Fisher information for deterministic systems (2023) Chaos 33, 103139.
[3] Swetamber Das and Jason R. Green. Maximum speed of dissipation (under review, 2023).
[4] Swetamber Das and Jason R. Green. Density matrix formulation of dynamical systems. Phys. Rev. E, 106:054135 (2022).
[5] Swetamber Das and Jason R. Green. Spectral bounds on Lyapunov exponents and entropy production in determin- istic dynamical systems (under review, 2023).