Microscopically Reversible Pathways with Memory
Statistical mechanics is a physics theory that deals with ensembles of microstates of a system compatible with environmental constraints and that on average define a thermodynamic state. The evolution of a small system is normally subjected to changing constraints, as set by a protocol, and involves...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/2/127 |
| _version_ | 1797414854316785664 |
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| author | Jose Ricardo Arias-Gonzalez |
| author_facet | Jose Ricardo Arias-Gonzalez |
| author_sort | Jose Ricardo Arias-Gonzalez |
| collection | DOAJ |
| description | Statistical mechanics is a physics theory that deals with ensembles of microstates of a system compatible with environmental constraints and that on average define a thermodynamic state. The evolution of a small system is normally subjected to changing constraints, as set by a protocol, and involves a stochastic dependence on previous events. Here, we generalize the dynamic trajectories described by a realization of a physical system without dissipation to include those in which the history of previous events is necessary to understand its future. This framework is then used to characterize the processes experienced by the stochastic system, as derived from ensemble averages over the available pathways. We find that the pathways that the system traces in the presence of a protocol entail different statistics from those in its absence and prove that both types of pathways are equivalent in the limit of independent events. Such equivalence implies that a thermodynamic system cannot evolve away from equilibrium in the absence of memory. These results are useful to interpret single-molecule experiments in biophysics and other fields in nanoscience, as well as an adequate platform to describe non-equilibrium processes. |
| first_indexed | 2024-03-09T05:39:56Z |
| format | Article |
| id | doaj.art-3af59af3229a4c61820deb722b58833e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:39:56Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3af59af3229a4c61820deb722b58833e2023-12-03T12:25:39ZengMDPI AGMathematics2227-73902021-01-019212710.3390/math9020127Microscopically Reversible Pathways with MemoryJose Ricardo Arias-Gonzalez0Centro de Tecnologías Físicas, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainStatistical mechanics is a physics theory that deals with ensembles of microstates of a system compatible with environmental constraints and that on average define a thermodynamic state. The evolution of a small system is normally subjected to changing constraints, as set by a protocol, and involves a stochastic dependence on previous events. Here, we generalize the dynamic trajectories described by a realization of a physical system without dissipation to include those in which the history of previous events is necessary to understand its future. This framework is then used to characterize the processes experienced by the stochastic system, as derived from ensemble averages over the available pathways. We find that the pathways that the system traces in the presence of a protocol entail different statistics from those in its absence and prove that both types of pathways are equivalent in the limit of independent events. Such equivalence implies that a thermodynamic system cannot evolve away from equilibrium in the absence of memory. These results are useful to interpret single-molecule experiments in biophysics and other fields in nanoscience, as well as an adequate platform to describe non-equilibrium processes.https://www.mdpi.com/2227-7390/9/2/127non-markovianmemorypathwaystochasticmicroscopic reversibilitystatistical mechanics |
| spellingShingle | Jose Ricardo Arias-Gonzalez Microscopically Reversible Pathways with Memory Mathematics non-markovian memory pathway stochastic microscopic reversibility statistical mechanics |
| title | Microscopically Reversible Pathways with Memory |
| title_full | Microscopically Reversible Pathways with Memory |
| title_fullStr | Microscopically Reversible Pathways with Memory |
| title_full_unstemmed | Microscopically Reversible Pathways with Memory |
| title_short | Microscopically Reversible Pathways with Memory |
| title_sort | microscopically reversible pathways with memory |
| topic | non-markovian memory pathway stochastic microscopic reversibility statistical mechanics |
| url | https://www.mdpi.com/2227-7390/9/2/127 |
| work_keys_str_mv | AT josericardoariasgonzalez microscopicallyreversiblepathwayswithmemory |