Measuring thermodynamic length.

@article{Crooks2007MeasuringTL,
  title={Measuring thermodynamic length.},
  author={Gavin E. Crooks},
  journal={Physical review letters},
  year={2007},
  volume={99 10},
  pages={
          100602
        }
}
  • G. Crooks
  • Published 2007
  • Physics, Medicine
  • Physical review letters
Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information, and Rao's entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out of equilibrium. In this Letter, we will consider how to define… Expand
Far-from-equilibrium measurements of thermodynamic length.
TLDR
This work shows how to measure thermodynamic length in far-from-equilibrium experiments using the work fluctuation relations, and extends Bennett's method to determine the potential of the mean force, as well as the thermodynamics length, in single-molecule experiments. Expand
Thermodynamic metrics and optimal paths.
TLDR
A friction tensor is derived that induces a Riemannian manifold on the space of thermodynamic states that controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties within the linear-response regime. Expand
Metrics and Energy Landscapes in Irreversible Thermodynamics
We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold’s, has achieved widespread use. Lengths calculated based on this metric have been used to boundExpand
Thermodynamic length in open quantum systems
The dissipation generated during a quasistatic thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocolsExpand
Non-equilibrium statistical mechanics: partition functions and steepest entropy increase
On the basis of just the microscopic definition of thermodynamic entropy and the definition of the rate of entropy increase as the sum of products of thermodynamic fluxes and their conjugated forces,Expand
Stochastic Thermodynamic Interpretation of Information Geometry.
  • Sosuke Ito
  • Mathematics, Medicine
  • Physical review letters
  • 2018
TLDR
A new link between stochastic thermodynamics and information theory well-known as information geometry is found and an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost. Expand
Investigation of the statistical distance to reach stationary distributions
Abstract The thermodynamic length gives a Riemannian metric to a system's phase space. Here we extend the traditional thermodynamic length to the information length ( L ) out of equilibrium andExpand
Contact Symmetries and Hamiltonian Thermodynamics
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related toExpand
Information geometry and non-equilibrium thermodynamic relations in the over-damped stochastic processes
  • Eun-jin Kim
  • Physics
  • Journal of Statistical Mechanics: Theory and Experiment
  • 2021
An advantageous method for understanding complexity is information geometry theory. In particular, a dimensionless distance, called information length L , permits us to describe time-varying,Expand
The Fisher Thermodynamics of Quasi-Probabilities
TLDR
This work investigates the thermal statistics of quasi-probabilities's semi-classical analogs in phase space for the important case of quadratic Hamiltonians, focusing attention in the three more important instances of Wigner, $P$-, and Husimi distributions. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 76 REFERENCES
On the relation between entropy and energy versions of thermodynamic length
The second derivative matrices of internal energy or of entropy may be used to define a metric structure on the set of equilibrium states of a thermodynamic system. When expressed relative to theExpand
Thermodynamic metric and stochastic measures
A modification of the thermodynamic Weinhold metric is introduced by the statistical scheme of bit-number cumulants discussed in earlier papers. It is a metric in the space of intensive thermalExpand
Thermodynamic length and dissipated availability
New expressions for the availability dissipated in a finite-time endoreversible process are found by use of Weinhold's metric on equilibrium states of a thermodynamic system. In particular, theExpand
Quasistatic processes as step equilibrations
The proportionality between the square of the distance traversed as measured in thermodynamic length and the minimum associated dissipation of a process is established in a new context independent ofExpand
Thermodynamics and an Introduction to Thermostatistics
GENERAL PRINCIPLES OF CLASSICAL THERMODYNAMICS. The Problem and the Postulates. The Conditions of Equilibrium. Some Formal Relationships, and Sample Systems. Reversible Processes and the Maximum WorkExpand
Geometrical aspects of statistical mechanics.
  • Brody, Rivier
  • Mathematics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
TLDR
The Riemannian geometrical approach to statistical mechanical systems due to Janyszek is applied to various models including the van der Waals gas and magnetic models and the scalar curvature for these models is shown to diverge not only at the critical points but also along the entire spinodal curve. Expand
Statistical distance and Hilbert space
A concept of "statistical distance" is defined between different preparations of the same quantum system, or in other words, between different rays in the same Hilbert space. Statistical distance isExpand
Metric geometry of equilibrium thermodynamics
It is shown that the principal empirical laws of equilibrium thermodynamics can be brought into correspondence with the mathematical axioms of an abstract metric space. This formal correspondenceExpand
Entropy differential metric, distance and divergence measures in probability spaces: A unified approach
The paper is devoted to metrization of probability spaces through the introduction of a quadratic differential metric in the parameter space of the probability distributions. For this purpose, aExpand
Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods.
TLDR
It is demonstrated that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements. Expand
...
1
2
3
4
5
...