Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit
We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass <i>N</i> sites and move energetically downhill while dissipating heat. Interestingly, we...
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MDPI AG
2023-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/8/1218 |
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| author | Henning Kirchberg Abraham Nitzan |
| author_facet | Henning Kirchberg Abraham Nitzan |
| author_sort | Henning Kirchberg |
| collection | DOAJ |
| description | We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass <i>N</i> sites and move energetically downhill while dissipating heat. Interestingly, we found that, starting from a discrete model, the limit in which the motion becomes continuous in space and time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>) is not unique and depends on what physical observables are assumed to be unchanged in the process. In particular, one may (as usually done) choose to keep the speed and diffusion coefficient fixed during this limiting process, in which case, the entropy production is affected. In addition, we also studied processes in which the entropy production is kept constant as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula> at the cost of a modified speed or diffusion coefficient. Furthermore, we also combined this dynamics with work against an opposing force, which made it possible to study the effect of discretization of the process on the thermodynamic efficiency of transferring the power input to the power output. Interestingly, we found that the efficiency was increased in the limit of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. Finally, we investigated the same process when transitions between sites can only happen at finite time intervals and studied the impact of this time discretization on the thermodynamic variables as the continuous limit is approached. |
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| format | Article |
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| language | English |
| last_indexed | 2024-03-10T23:57:50Z |
| publishDate | 2023-08-01 |
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| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f25611ba63d5469b81a8c0dae9141dcc2023-11-19T01:00:13ZengMDPI AGEntropy1099-43002023-08-01258121810.3390/e25081218Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous LimitHenning Kirchberg0Abraham Nitzan1Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, USADepartment of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, USAWe considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass <i>N</i> sites and move energetically downhill while dissipating heat. Interestingly, we found that, starting from a discrete model, the limit in which the motion becomes continuous in space and time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>) is not unique and depends on what physical observables are assumed to be unchanged in the process. In particular, one may (as usually done) choose to keep the speed and diffusion coefficient fixed during this limiting process, in which case, the entropy production is affected. In addition, we also studied processes in which the entropy production is kept constant as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula> at the cost of a modified speed or diffusion coefficient. Furthermore, we also combined this dynamics with work against an opposing force, which made it possible to study the effect of discretization of the process on the thermodynamic efficiency of transferring the power input to the power output. Interestingly, we found that the efficiency was increased in the limit of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. Finally, we investigated the same process when transitions between sites can only happen at finite time intervals and studied the impact of this time discretization on the thermodynamic variables as the continuous limit is approached.https://www.mdpi.com/1099-4300/25/8/1218thermodynamic processentropy productiondiscrete state spacecontinuous state spacestochastic thermodynamics |
| spellingShingle | Henning Kirchberg Abraham Nitzan Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit Entropy thermodynamic process entropy production discrete state space continuous state space stochastic thermodynamics |
| title | Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit |
| title_full | Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit |
| title_fullStr | Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit |
| title_full_unstemmed | Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit |
| title_short | Energy Conversion and Entropy Production in Biased Random Walk Processes—From Discrete Modeling to the Continuous Limit |
| title_sort | energy conversion and entropy production in biased random walk processes from discrete modeling to the continuous limit |
| topic | thermodynamic process entropy production discrete state space continuous state space stochastic thermodynamics |
| url | https://www.mdpi.com/1099-4300/25/8/1218 |
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