Thermodynamic speed limits from the regression of information
arXiv:2105.01588
Abstract
Irreversible processes accomplished in a fixed time involve nonlinearly coupled flows of matter, energy, and information. Here, using entropy production as an example, we show how thermodynamic uncertainty relations and speed limits on these nonlinear processes derive from linear regression. These uncertainty relations hold for both passive and actively-driven nonequilibrium processes and all have a mathematical form that mirrors uncertainty relations in quantum mechanics. Using optimal linear models, we show that information-theoretic variables naturally give physical predictions of the equation of motion on statistical manifolds in terms of physical observables. In these models, optimal intercepts are related to nonequilibrium analogs of Massieu functions/thermodynamic potentials, and optimal slopes are related to speed limits on collections of thermodynamic observables. Within this formalism, the second law of thermodynamics has a geometric interpretation as the nonnegativity of the slope and constrains the equation of motion. Overall, our results suggest that unknown relationships between nonequilibrium variables can be learned through statistical-mechanical inference.
References in corpus (16)
- Thermodynamic uncertainty relation for biomolecular processes
- Dissipation bounds all steady-state current fluctuations
- Quantum speed limit for non-Markovian dynamics
- Measuring thermodynamic length
- Second law and Landauer principle far from equilibrium
- Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
- Finite-time generalization of the thermodynamic uncertainty relation
- Thermodynamics of precision in quantum non equilibrium steady states
- Multidimensional thermodynamic uncertainty relations
- Uncertainty relations in stochastic processes: An information inequality approach
- The dissipation-time uncertainty relation
- Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
- Frenetic bounds on the entropy production
- Uncertainty relations for underdamped Langevin dynamics
- A generalization of Margolus-Levitin bound
- Limits of Predictions in Thermodynamic Systems: A Review