Nonequilibrium thermodynamics of uncertain stochastic processes

Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world experiment there is non-zero uncertainty about the precise value of temperatures, chemical potentials, energy spectrum, etc. Here we investigate how this uncertainty modifies the theorems of stochastic thermodynamics. We consider two scenarios: in the an (called effective ) scenario we fix the (unknown, randomly generated) experimental apparatus and then repeatedly observe (stochastic) trajectories of the system for that fixed apparatus. In contrast, in a (called phenomenological ) scenario the (unknown) apparatus is re-generated for each trajectory. We derive expressions for thermodynamic quantities in both scenarios. We also discuss the physical interpretation of effective (scenario) entropy production (EP), derive the effective mismatch cost, and provide a numerical analysis of the effective thermodynamics of a quantum dot implementing bit erasure with uncertain temperature. We then analyze the protocol for moving between two state distributions that maximizes effective work extraction. Next we investigate the effective thermodynamic value of information, focusing on the case where there is a delay between initialization of the system and the start of the protocol. Finally, we derive the detailed and integrated fluctuation theorems (FTs) for the phenomenological EP. In particular, we show how the phenomenological FTs account for the fact that the longer a trajectory runs, the more information it provides concerning the precise experimental apparatus, and therefore the less EP it generates.

[1]  D. Wolpert,et al.  Entropy production and thermodynamics of information under protocol constraints , 2020, ArXiv.

[2]  P. Riechers,et al.  Initial-state dependence of thermodynamic dissipation for any quantum process. , 2020, Physical review. E.

[3]  P. Hänggi,et al.  Comment on "Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force". , 2020, Physical review. E.

[4]  M. Esposito,et al.  Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force. , 2020, Physical review. E.

[5]  P. Hänggi,et al.  Colloquium : Statistical mechanics and thermodynamics at strong coupling: Quantum and classical , 2019, 1911.11660.

[6]  David H. Wolpert,et al.  The stochastic thermodynamics of computation , 2019, Journal of Physics A: Mathematical and Theoretical.

[7]  C. E. Fiore,et al.  Entropy production and heat capacity of systems under time-dependent oscillating temperature. , 2019, Physical review. E.

[8]  Massimiliano Esposito,et al.  Detailed Fluctuation Theorems: A Unifying Perspective , 2018, Entropy.

[9]  Artemy Kolchinsky,et al.  Semantic information, autonomous agency and non-equilibrium statistical physics , 2018, Interface Focus.

[10]  M. N. Bera,et al.  Thermodynamics from Information , 2018, 1805.10282.

[11]  Krzysztof Ptaszyński.  First-passage times in renewal and nonrenewal systems. , 2018, Physical review. E.

[12]  S. Davis,et al.  Temperature is not an observable in superstatistics , 2016, Physica A: Statistical Mechanics and its Applications.

[13]  Todd R. Gingrich,et al.  Hierarchical bounds on entropy production inferred from partial information , 2017, 1708.06769.

[14]  M. Esposito,et al.  Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining. , 2017, Physical review. E.

[15]  D. Wolpert,et al.  Dependence of dissipation on the initial distribution over states , 2016, 1607.00956.

[16]  U. Seifert.  First and Second Law of Thermodynamics at Strong Coupling. , 2015, Physical review letters.

[17]  David H. Wolpert,et al.  Extending Landauer's Bound from Bit Erasure to Arbitrary Computation , 2015, 1508.05319.

[18]  T. Sagawa,et al.  Role of measurement-feedback separation in autonomous Maxwell's demons , 2015, 1501.06071.

[19]  Massimiliano Esposito,et al.  Ensemble and trajectory thermodynamics: A brief introduction , 2014, 1403.1777.

[20]  Takahiro Sagawa,et al.  Role of mutual information in entropy production under information exchanges , 2013, 1307.6092.

[21]  M. Esposito,et al.  Finite-time erasing of information stored in fermionic bits. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  U. Seifert.  Stochastic thermodynamics, fluctuation theorems and molecular machines , 2012, Reports on progress in physics. Physical Society.

[23]  Masahito Ueda,et al.  Nonequilibrium thermodynamics of feedback control. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Katharina Krischer,et al.  Superstatistics in nanoscale electrochemical systems , 2011, Proceedings of the National Academy of Sciences.

[25]  Stefan Thurner,et al.  Generalized entropies and the transformation group of superstatistics , 2011, Proceedings of the National Academy of Sciences.

[26]  M. Esposito,et al.  Three faces of the second law. I. Master equation formulation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Massimiliano Esposito,et al.  Entropy production as correlation between system and reservoir , 2009, 0908.1125.

[28]  H. Hasegawa,et al.  Generalization of the Second Law for a Nonequilibrium Initial State , 2009, 0907.1569.

[29]  J. Parrondo,et al.  Entropy production and the arrow of time , 2009, 0904.1573.

[30]  Masahito Ueda,et al.  Minimal energy cost for thermodynamic information processing: measurement and information erasure. , 2008, Physical review letters.

[31]  M. Feito,et al.  Thermodynamics of feedback controlled systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  J. Parrondo,et al.  Lower bounds on dissipation upon coarse graining. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  J. Parrondo,et al.  Dissipation: the phase-space perspective. , 2007, Physical review letters.

[34]  A. M. Mathai,et al.  Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy , 2006, cond-mat/0607605.

[35]  F. Sattin.  Bayesian approach to superstatistics , 2006, cond-mat/0601154.

[36]  C. Beck.  Stretched exponentials from superstatistics , 2005, cond-mat/0510841.

[37]  S. Sasa,et al.  Stochastic energetics of non-uniform temperature systems , 1998, cond-mat/9810220.

[38]  David H. Wolpert,et al.  On the Use of Evidence in Neural Networks , 1992, NIPS.

[39]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[40]  S. Kirkpatrick,et al.  Solvable Model of a Spin-Glass , 1975 .

[41]  K. Adkins.  Theory of spin glasses , 1974 .