Decomposition of metric tensor in thermodynamic geometry in terms of relaxation timescales
arXiv:2409.08546 · doi:10.1103/PhysRevE.111.034113
Abstract
Geometrical methods are extensively applied to thermodynamics including stochastic thermodynamics. In the case of slow-driving linear response regime, a geometrical framework, known as thermodynamic geometry, is established. The key of this framework is the thermodynamic length characterized by a metric tensor defined on the space of controlling variables. As the metric tensor is given in terms of the equilibrium time-correlation functions of the thermodynamic forces, it contains the information of timescales, which may be useful for analyzing the performance of heat engines. In this paper, we show that the metric tensor for underdamped Langevin dynamics can be decomposed in terms of the relaxation times of a system itself, which govern the timescales of the equilibrium time-correlation functions of the thermodynamic forces. As an application of the decomposition of the metric tensor, we demonstrate that it is possible to achieve Carnot efficiency at finite power by taking the vanishing limit of relaxation times without breaking trade-off relations between efficiency and power of heat engines in terms of thermodynamic geometry.
12 pages, 3 figures
References in corpus (21)
- Optimal finite-time processes in stochastic thermodynamics
- Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
- Finite-time Landauer principle
- The geometry of thermodynamic control
- Finite-Time Quantum Landauer Principle and Quantum Coherence
- Thermodynamic control -- an old paradigm with new applications
- Optimal Control in Stochastic Thermodynamics
- Thermodynamic geometry of minimum-dissipation driven barrier crossing
- A geometric bound on the efficiency of irreversible thermodynamic cycles
- Geometry of work fluctuations versus efficiency in microscopic thermal machines
- Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
- A unified, geometric framework for nonequilibrium protocol optimization
- Optimal finite-time Brownian Carnot engine
- Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines
- Minimally dissipative information erasure in a quantum dot via thermodynamic length
- Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
- Achieving Carnot efficiency in a finite-power Brownian Carnot cycle with arbitrary temperature difference
- Optimal Control of Underdamped Systems: An Analytic Approach
- Compatibility of Carnot efficiency with finite power in an underdamped Brownian Carnot cycle in small temperature-difference regime
- Reliability and operation cost of underdamped memories during cyclic erasures
- Geometric characterization for cyclic heat engines far from equilibrium