# Measuring thermodynamic length.

@article{Crooks2007MeasuringTL, title={Measuring thermodynamic length.}, author={Gavin E. Crooks}, journal={Physical review letters}, year={2007}, volume={99 10}, pages={ 100602 } }

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

#### Topics from this paper

#### Paper Mentions

#### 223 Citations

Far-from-equilibrium measurements of thermodynamic length.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2009

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.

- Medicine, Physics
- Physical review letters
- 2012

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

- Computer Science, Mathematics
- Entropy
- 2015

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 bound… Expand

Thermodynamic length in open quantum systems

- Physics
- Quantum
- 2019

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 protocols… Expand

Non-equilibrium statistical mechanics: partition functions and steepest entropy increase

- Mathematics
- 2011

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.

- Mathematics, Medicine
- Physical review letters
- 2018

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

- Physics
- 2015

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 and… Expand

Contact Symmetries and Hamiltonian Thermodynamics

- Physics, Mathematics
- 2014

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 to… Expand

Information geometry and non-equilibrium thermodynamic relations in the over-damped stochastic processes

- 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

- Mathematics, Computer Science
- Entropy
- 2015

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

#### References

SHOWING 1-10 OF 76 REFERENCES

On the relation between entropy and energy versions of thermodynamic length

- Chemistry
- 1984

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 the… Expand

Thermodynamic metric and stochastic measures

- Physics
- 1985

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 thermal… Expand

Thermodynamic length and dissipated availability

- Mathematics
- 1983

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, the… Expand

Quasistatic processes as step equilibrations

- Chemistry
- 1985

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 of… Expand

Thermodynamics and an Introduction to Thermostatistics

- Mathematics, Materials Science
- 1960

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 Work… Expand

Geometrical aspects of statistical mechanics.

- Mathematics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

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

- Physics
- 1981

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 is… Expand

Metric geometry of equilibrium thermodynamics

- Chemistry
- 1975

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 correspondence… Expand

Entropy differential metric, distance and divergence measures in probability spaces: A unified approach

- Mathematics
- 1982

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, a… Expand

Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods.

- Mathematics, Medicine
- Physical review letters
- 2003

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