Maxwell’s Demons with Finite Size and Response Time

Abstract

Nearly all theoretical analyses of the Maxwell's demon focus on its energetic and entropic costs of operation. Here, we focus on its rate of operation. In our model, a demon's rate limitation stems from its finite response time and gate area. We determine the rate limits of mass and energy transfer, as well as entropic reduction for four such demons: Those that select particles according to (1) direction, (2) energy, (3) number and (4) entropy. Lastly, we determine the optimal gate size for a demon with small, finite response time, and compare our predictions with molecular dynamics simulations with both ideal and non-ideal gasses. Lastly, we study the conditions under which the demons are able to move both energy and particles in the chosen direction when attempting to only move one. arXiv:1903.05724v4 [cond-mat.stat-mech]

Predictive Maxwell's demons

“…Some authors describe the computational process within the demon as manipulations of a tape bits [12][13][14][15] or qubits [16], while others consider demons that manipulate microstates by fully mechanical means [17][18][19]. Models of non-ideal demons [12,13] account for the thermal equilibriation of the demon with the system, the demon's finite mass [19], or finite size and response time [20]. Recently experimental constructions have also become feasible [21][22][23][24][25][26][27][28][29][30][31][32].…”

“…Previously, we studied how the finite size and response time constrains a demon's heat and mass transport rate [20]. However, our model demon only used local information, and did not take into consideration future arrivals.…”

“…Non-Predictive Demons. Our definition of the nonpredictive demon comes from a previous work [20], where we studied demons with finite size A and response time τ . We start with a brief overview of the demon model, which will be identical for both the predictive and nonpredictive cases.…”

“…The probability that n particles are incident on the gate during a length of time τ follows a Poisson distribution with a Poisson parameter [20],…”

“…The rates ν l , ν r are crucial in characterizing the demons' performance. For example, the average energy and number currents for non-predictive demons with small response time τ are [20] Ė(d)…”