Trajectory Class Fluctuation Theorem
Abstract: The Trajectory Class Fluctuation Theorem (TCFT) substantially strengthens the Second Law of Thermodynamics -- that, in point of fact, can be a rather weak bound on resource fluxes. Practically, it improves empirical estimates of free energies, a task known to be statistically challenging, and has diagnosed successful and failed information processing in experimentally-implemented Josephson-junction information engines. The development here justifies that empirical analysis, explicating its mathematical foundations. The TCFT reveals the thermodynamics induced by macroscopic system transformations for each measurable subset of system trajectories. In this, it directly combats the statistical challenge of extremely rare events that dominate thermodynamic calculations. And, it reveals new forms of free energy -- forms that can be solved for analytically and practically estimated. Conceptually, the TCFT unifies a host of previously-established fluctuation theorems, interpolating from Crooks' Detailed Fluctuation Theorem (single trajectories) to Jarzynski's Equality (trajectory ensembles).
- Probability of second law violations in shearing steady flows. Phys. Rev. Lett., 71:2401–2404, 1993.
- G. Gallavotti and E. G. D. Cohen. Dynamical ensembles in nonequilibrium statistical mechanics. Phys. Rev. Lett., 74:2694–2697, 1995.
- C. Jarzynski. Nonequilibrium equality for free energy differences. Phys. Rev. Lett., 78(14):2690–2693, 1997.
- G. E. Crooks. Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys. Rev. E, 60:2721, 1999.
- C. Jarzynski. Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale. Ann. Rev. Cond. Matter Physics, 2(1):329–351, 2011.
- G. E. Crooks. Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems. J. Stat. Phys., 90(5/6):1481–1487, 1998.
- C. Jarzynski. Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech.: Theor. Exp., 2004(09):P09005, 2004.
- Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski’s equality. Science, 296:1832, 2002.
- A differential fluctuation theorem. J. Phys. Chem. B, 112(19):6168–6174, 2008.
- Recovery of free energy branches in single molecule experiments. Phys. Rev. Lett., 102(7):070602, 2009.
- S. Deffner and E. Lutz. Nonequilibrium work distribution of a quantum harmonic oscillator. Phys. Rev. E, 77(2):021128, 2008.
- C. Jarzynski. Rare events and the convergence of exponentially averaged work values. Phys. Rev. E, 73(4):046105, 2006.
- S. Asban and S. Rahav. Nonequilibrium free-energy estimation conditioned on measurement outcomes. Phys. Rev. E, 96(2):022155, 2017.
- Harnessing fluctuations in thermodynamic computing via time-reversal symmetries. Phys. Rev. Res., 3(3):033115, 2021.
- Thermodynamics of information. Nature Physics, 11(2):131–139, 2015.
- G. E. Crooks. Excursions in statistical dynamics. PhD thesis, University of California, Berkeley, 1999.
- U. Seifert. Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys., 75:126001, 2012.
- C. Jarzynski. Hamiltonian derivation of a detailed fluctuation theorem. J. Stat. Phys., 98(1-2):77–102, 2000.
- U. Seifert. Entropy production along a stochastic trajectory and an integral fluctuation theorem. Phys. Rev. Lett., 95(4):040602, 2005.
- Lower bounds on dissipation upon coarse graining. Phys. Rev. E, 78(1):011107, 2008.
- Balancing error and dissipation in computing. Physical Review Research, 2(3):033524, 2020.
- Refining Landauer’s stack: Balancing error and dissipation when erasing information. J. Stat. Physics, 183(1):1–23, 2021.
- É. Roldán and J. M. R. Parrondo. Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems. Phys. Rev. E, 85(3):031129, 2012.
- Inferring broken detailed balance in the absence of observable currents. Nature Comm.unications, 10(1):1–10, 2019.
- D. J. Skinner and J. Dunkel. Estimating entropy production from waiting time distributions. Phys. Rev. Let., 127(19):198101, 2021.
- Dissipation: The phase-space perspective. Phys. Rev. L, 98(8):080602, 2007.
- S. Vaikuntanathan and C. Jarzynski. Dissipation and lag in irreversible processes. Euro. Phys. Let., 87(6):60005, 2009.
- Detailed Jarzynski equality applied to a logically irreversible procedure. Euro. Phys. Let., 103:60002, 2013.
- G. E. Crooks. Path-ensemble averages in systems driven far from equilibrium. Phys. Rev. E, 61(3):2361–2366, 2000.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.