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 N 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 (N & RARR;& INFIN;) 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 N & RARR;& INFIN; 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 N & RARR;& INFIN;. 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.

Automated summary

In this study, we examined the discrete and continuous representations of a thermodynamic process involving a random walker using energy to move downhill. We found that the uniqueness of the continuous limit depended on the assumptions made about unchanged physical observables during the process. Additionally, we investigated the impact of discretization on thermodynamic efficiency and observed an increase in efficiency as the process approached the continuous limit.