Biological sensory receptors provide excellent examples of microscopic scale information transduc... more Biological sensory receptors provide excellent examples of microscopic scale information transduction amidst stochastic noise. We argue that stochasticity is not always a hindrance to sensing. Instead, it could allow a single stochastic sensor to perform multiplexing: simultaneously transducing multiple types of environmental information to the downstream sensory network. Through a Langevin dynamics simulation of a ligand-receptor sensor in a bath of ligands, we demonstrate that a binary-state receptor can simultaneously encode multiple independent environmental variables, such as ligand concentration and the speed of media flow. We develop a general theory of stochastic sensory multiplexing and suggest two theoretical upper bounds. Furthermore, we conjecture that randomly generated sensors typically saturate the tighter upper bound. The theoretical framework developed in this study, which involves a rank-deficient maximum likelihood analysis (rd-MLE), provides a systematic approach to comprehensively assess a sensor's sensory ability without any initial assumptions. This theoretical framework can inspire the design of more efficient artificial sensors.
Biological sensory receptors provide excellent examples of microscopic scale information transduc... more Biological sensory receptors provide excellent examples of microscopic scale information transduction amidst stochastic noise. We argue that stochasticity is not always a hindrance to sensing. Instead, it could allow a single stochastic sensor to perform multiplexing: simultaneously transducing multiple types of environmental information to the downstream sensory network. Through a Langevin dynamics simulation of a ligand-receptor sensor in a bath of ligands, we demonstrate that a binary-state receptor can simultaneously encode multiple independent environmental variables, such as ligand concentration and the speed of media flow. We develop a general theory of stochastic sensory multiplexing and suggest two theoretical upper bounds. Furthermore, we conjecture that randomly generated sensors typically saturate the tighter upper bound. The theoretical framework developed in this study, which involves a rank-deficient maximum likelihood analysis (rd-MLE), provides a systematic approach to comprehensively assess a sensor's sensory ability without any initial assumptions. This theoretical framework can inspire the design of more efficient artificial sensors.
Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harn... more Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harness energy from the oscillatory bath and use it to drive other processes. Using a novel geometrical approach, under fast temperature oscillation, we derive a general design principle for obtaining the optimal catalytic energy landscape that can harness energy from a temperature-oscillatory bath and use it to invert a spontaneous reaction. By driving the reaction against the spontaneous direction, the catalysts convert low free energy product molecules to high free energy reactant molecules. The design principle, derived for arbitrary cyclic catalysts, is expressed as a simple quadratic objective function that only depends on the reaction activation energies, and is independent of the temperature protocol. Since the reaction activation energies are directly accessible by experimental measurements, the objective function can be directly used to guide the search for optimal energyharvesting catalysts.
Nonequilibrium transportation of particles through a restricted space (such as porous media or na... more Nonequilibrium transportation of particles through a restricted space (such as porous media or narrow channels) significantly differs from free space. With a simple model of two types of particles competing to transport via a passive single-lane channel connecting two chemical baths, we find two dynamical modes of transportation-the dud mode and the ratchet mode. At the ratchet mode, the gradient flow of one type of particle forces the other into a transient antiequilibrium flow against its gradient. At the dud mode, the two types of particles both flow according to their gradients. This counterintuitive nonequilibrium effect can be explained by a sloppy gear mechanism. In addition to the antigradient flow observed in the ratchet mode, we find that the nonequilibrium sloppy gear mechanism suppresses the flow of one particle while allowing the flow for the other. This mechanism provides a general theoretical framework to explain and design the selective transportation of particles via passive channels.
Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probab... more Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probability a priori where thermodynamic infinite-size limit is replaced by multiple-measurement limit. A duality symmetry between Massieu's and Gibbs' entropy arises in the limit of infinitely repeated observations, yielding the Gibbs equation and Hill-Gibbs-Duhem equation (HGDE) as dual pair. If a system has thermodynamic limit satisfying Callen's postulate, entropy being an Eulerian function, the symmetry is lost: the HGDE reduces to the Gibbs-Duhem equation. This theory provides a de-mechanized foundation for classical and nanothermodynamics and offers a framework for distilling emergence from large data, free from underlying details.
The theory of probability shows that, as the fraction Xn/Y → 0, the conditional probability for X... more The theory of probability shows that, as the fraction Xn/Y → 0, the conditional probability for Xn, given Xn+Y ∈ hδ := [h, h+δ], has a limit law fXn(x)enδ, whereψn(hδ) equals to [∂ lnP (Y ∈ yδ)/∂y]y=h plus an additional term, contributed from the correlation between Xn and bath Y . By applying this limit law to a composite heterogeneous system including a system of interest and a large but finite bath, we derive a pseudo-Hamiltonian and a corresponding generalized Boltzmann distribution law. This result is applicable to the system of arbitrary size, and also allows for strong system-bath interactions. In contrast to previous results derived with the help of an additional larger bath and a pre-determined temperature, our approach treats the composite system as an isolated system. It allows us to derive a temperature and corrections to the temperature due to the strong system-bath coupling when the bath size is not infinity. Furthermore, we discuss the thermodynamic relation of free e...
Thermodynamic laws are limiting behavior of the statistics of repeated measurements of an arbitra... more Thermodynamic laws are limiting behavior of the statistics of repeated measurements of an arbitrary system with a priori probability distribution. A duality symmetry arises, between Massieu-Guggenheim entropy and Gibbs entropy, in the limit of large number of measurements. This yields the fundamental thermodynamic relation and Hill-Gibbs-Duhem (HGD) equation as a dual pair. We show if the system itself has a second macroscopic limit that satisfies Callen's postulate that entropy being an Eulerian homogeneous function of all extensive variables, the symmetry is lost: the HGD equation reduces to the Gibbs-Duhem equation. This theory provides better logic to textbook thermodynamics, a clarification on nanothermodynamics, as well as novel ideas for a thermodynamic-like framework for single-cell biology.
In living cells, ion channels passively allow for ions to flow through as the concentration gradi... more In living cells, ion channels passively allow for ions to flow through as the concentration gradient relax to thermal equilibrium. Most ion channels are selective, only allowing one type of ion to go through while blocking another. One salient example is KcsA, which allows for larger K ions through but blocks the smaller Na ions. This counter-intuitive selectivity has been explained by two distinct theories that both focus on equilibrium properties: particle-channel affinity and particlesolvent affinity. However, ion channels operate far from equilibrium. By constructing minimal kinetic models of channels, we discover a ubiquitous kinetic ratchet effect as a non-equilibrium mechanism to explain such selectivity. We find that a multi-site channel kinetically couples the competing flows of two types of particles, where one particle’s flow could suppress or even invert the flow of another type. At the inversion point (transition between the ratchet and dud modes), the channel achieves ...
Proceedings of the National Academy of Sciences, 2017
Significance It is commonly expected that cooling a hot system takes a longer time than cooling a... more Significance It is commonly expected that cooling a hot system takes a longer time than cooling an identical system initiated at a lower temperature. Surprisingly, this is not always the case; in various systems, including water and magnetic alloys, it has been observed that a hot system can be cooled faster. These anomalous cooling effects are referred to as “the Mpemba effect”, and so far they lack a generic details-independent explanation. Based on recent developments in the theory of nonequilibrium thermodynamics, we propose a generic mechanism for similar effects, demonstrate it in various systems, and predict a similar anomalous behavior in heating. Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon—the “Mpemba effect”—was first observed in water and has recently been reported in other systems. Whereas several detail-dependent explanations were suggested for some of these observa...
Steady dissipation of energy is a crucial property that distinguishes active particles from Brown... more Steady dissipation of energy is a crucial property that distinguishes active particles from Brownian particles. However, it is not straightforward to explicitly model the dissipative property of existing active particles driven by a vibrating plate. We present a novel active particle that can be explicitly modeled by Newtonian dynamics of a conservative force field plus two asymmetrical dissipative terms. The particle is a dimer consisting of two ping-pong balls connected by a rigid rod, and its two balls are filled with granular particles of the same total mass but of different grain size. This dimer placed on a vibrating plate exhibits 3 types of motion – by tuning the frequency and the amplitude of the vibration, the dimer undergoes either a directed motion toward the small (or large) grain-filled side or an unbiased random motion. We investigate the various modes of motion both experimentally and numerically and show that the directed motion is a result of the asymmetric damping...
Statistical estimation theory determines the optimal way of estimating parameters of a fluctuatin... more Statistical estimation theory determines the optimal way of estimating parameters of a fluctuating noisy signal. However, if the estimation is performed on unreliable hardware, a sub-optimal estimation procedure can outperform the previously optimal procedure. Here, we compare classes of circadian clocks by viewing them as phase estimators for the periodic day-night light signal. We find that continuous attractor-based free running clocks, such as those found in the cyanobacterium Synechococcus elongatus and humans, are nearly optimal phase estimators since their flat attractor directions efficiently project out light intensity fluctuations due to weather patterns (`external noise'). However, such flat directions also make these continuous limit cycle attractors highly vulnerable to diffusive 'internal noise'. Given such unreliable biochemical hardware, we find that point attractor-based damped clocks, such as those found in a smaller cyanobacterium with low protein copy...
Continuous attractors have been used to understand recent neuroscience experiments where persiste... more Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions under which the emergent bump of neural activity in such networks can be manipulated by space and time-dependent external sensory or motor signals are not understood. Here, we find fundamental limits on how rapidly internal representations encoded along continuous attractors can be updated by an external signal. We apply these results to place cell networks to derive a velocity-dependent nonequilibrium memory capacity in neural networks.
Recent developments in nonequilibrium statistical mechanics suggest that the history of entropy p... more Recent developments in nonequilibrium statistical mechanics suggest that the history of entropy production in a system determines the relative likelihood of competing processes. This presents the possibility of interpreting and predicting the self-organization of complex active systems, but existing theories rely on quantities that are challenging to obtain. Here, we address this issue for a general class of Markovian systems in which two types of self-replicating molecular assemblies (self-replicators) compete for a pool of limiting resource molecules within a nonequilibrium steady state. We derive exact relations that show that the relative fitness of these species depends on a path function, ψ, which is a sum of the entropy production and a relative-entropy term. In the limit of infinite path length, ψ reduces to the entropy production. We demonstrate use of the theory by numerically studying two models inspired by biological systems, including a simplified model of a competition between strains of the yeast prion Sup35 in the presence of driven disaggregation by the ATPase Hsp104.
We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a... more We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere [1], but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of $\pi$. If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer's eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously pe...
Many organisms use free running circadian clocks to anticipate the day night cycle. However, othe... more Many organisms use free running circadian clocks to anticipate the day night cycle. However, others organisms use simple stimulus-response strategies ('hourglass clocks') and it is not clear when such strategies are sufficient or even preferable to free running clocks. Here, we find that free running clocks, such as those found in the cyanobacterium and humans, can efficiently project out light intensity fluctuations due to weather patterns ('external noise') by exploiting their limit cycle attractor. However, such limit cycles are necessarily vulnerable to 'internal noise'. Hence, at sufficiently high internal noise, point attractor-based 'hourglass' clocks, such as those found in a smaller cyanobacterium with low protein copy number, , can outperform free running clocks. By interpolating between these two regimes in a diverse range of oscillators drawn from across biology, we demonstrate biochemical clock architectures that are best suited to differ...
We extend a generalized integral fluctuation relation in diffusion processes that we obtained pre... more We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation. This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.
Proceedings of the National Academy of Sciences, 2017
Significance It is commonly expected that cooling a hot system takes a longer time than cooling a... more Significance It is commonly expected that cooling a hot system takes a longer time than cooling an identical system initiated at a lower temperature. Surprisingly, this is not always the case; in various systems, including water and magnetic alloys, it has been observed that a hot system can be cooled faster. These anomalous cooling effects are referred to as “the Mpemba effect”, and so far they lack a generic details-independent explanation. Based on recent developments in the theory of nonequilibrium thermodynamics, we propose a generic mechanism for similar effects, demonstrate it in various systems, and predict a similar anomalous behavior in heating.
land at College Park -We describe a method to compute the Helmholtz free energy of a crystalline ... more land at College Park -We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the manydimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of 10 -5 k B T per particle.
Title of dissertation: TOPICS IN EQUILIBRIUM AND NONEQUILIBRIUM THERMODYNAMICS: COMPUTING CRYSTAL... more Title of dissertation: TOPICS IN EQUILIBRIUM AND NONEQUILIBRIUM THERMODYNAMICS: COMPUTING CRYSTALLINE FREE ENERGIES AND ENGINEERING MAXWELL’S DEMON Zhiyue Lu, Doctor of Philosophy, 2015 Dissertation directed by: Professor Christopher Jarzynski Department of Chemistry and Biochemistry; Institute for Physical Science and Technology This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducin...
A simple model illustrates the operating principles of an information engine, a mechanical device... more A simple model illustrates the operating principles of an information engine, a mechanical device that mimics the behavior of Maxwell’s demon by converting heat into information plus work.
Biological sensory receptors provide excellent examples of microscopic scale information transduc... more Biological sensory receptors provide excellent examples of microscopic scale information transduction amidst stochastic noise. We argue that stochasticity is not always a hindrance to sensing. Instead, it could allow a single stochastic sensor to perform multiplexing: simultaneously transducing multiple types of environmental information to the downstream sensory network. Through a Langevin dynamics simulation of a ligand-receptor sensor in a bath of ligands, we demonstrate that a binary-state receptor can simultaneously encode multiple independent environmental variables, such as ligand concentration and the speed of media flow. We develop a general theory of stochastic sensory multiplexing and suggest two theoretical upper bounds. Furthermore, we conjecture that randomly generated sensors typically saturate the tighter upper bound. The theoretical framework developed in this study, which involves a rank-deficient maximum likelihood analysis (rd-MLE), provides a systematic approach to comprehensively assess a sensor's sensory ability without any initial assumptions. This theoretical framework can inspire the design of more efficient artificial sensors.
Biological sensory receptors provide excellent examples of microscopic scale information transduc... more Biological sensory receptors provide excellent examples of microscopic scale information transduction amidst stochastic noise. We argue that stochasticity is not always a hindrance to sensing. Instead, it could allow a single stochastic sensor to perform multiplexing: simultaneously transducing multiple types of environmental information to the downstream sensory network. Through a Langevin dynamics simulation of a ligand-receptor sensor in a bath of ligands, we demonstrate that a binary-state receptor can simultaneously encode multiple independent environmental variables, such as ligand concentration and the speed of media flow. We develop a general theory of stochastic sensory multiplexing and suggest two theoretical upper bounds. Furthermore, we conjecture that randomly generated sensors typically saturate the tighter upper bound. The theoretical framework developed in this study, which involves a rank-deficient maximum likelihood analysis (rd-MLE), provides a systematic approach to comprehensively assess a sensor's sensory ability without any initial assumptions. This theoretical framework can inspire the design of more efficient artificial sensors.
Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harn... more Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harness energy from the oscillatory bath and use it to drive other processes. Using a novel geometrical approach, under fast temperature oscillation, we derive a general design principle for obtaining the optimal catalytic energy landscape that can harness energy from a temperature-oscillatory bath and use it to invert a spontaneous reaction. By driving the reaction against the spontaneous direction, the catalysts convert low free energy product molecules to high free energy reactant molecules. The design principle, derived for arbitrary cyclic catalysts, is expressed as a simple quadratic objective function that only depends on the reaction activation energies, and is independent of the temperature protocol. Since the reaction activation energies are directly accessible by experimental measurements, the objective function can be directly used to guide the search for optimal energyharvesting catalysts.
Nonequilibrium transportation of particles through a restricted space (such as porous media or na... more Nonequilibrium transportation of particles through a restricted space (such as porous media or narrow channels) significantly differs from free space. With a simple model of two types of particles competing to transport via a passive single-lane channel connecting two chemical baths, we find two dynamical modes of transportation-the dud mode and the ratchet mode. At the ratchet mode, the gradient flow of one type of particle forces the other into a transient antiequilibrium flow against its gradient. At the dud mode, the two types of particles both flow according to their gradients. This counterintuitive nonequilibrium effect can be explained by a sloppy gear mechanism. In addition to the antigradient flow observed in the ratchet mode, we find that the nonequilibrium sloppy gear mechanism suppresses the flow of one particle while allowing the flow for the other. This mechanism provides a general theoretical framework to explain and design the selective transportation of particles via passive channels.
Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probab... more Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probability a priori where thermodynamic infinite-size limit is replaced by multiple-measurement limit. A duality symmetry between Massieu's and Gibbs' entropy arises in the limit of infinitely repeated observations, yielding the Gibbs equation and Hill-Gibbs-Duhem equation (HGDE) as dual pair. If a system has thermodynamic limit satisfying Callen's postulate, entropy being an Eulerian function, the symmetry is lost: the HGDE reduces to the Gibbs-Duhem equation. This theory provides a de-mechanized foundation for classical and nanothermodynamics and offers a framework for distilling emergence from large data, free from underlying details.
The theory of probability shows that, as the fraction Xn/Y → 0, the conditional probability for X... more The theory of probability shows that, as the fraction Xn/Y → 0, the conditional probability for Xn, given Xn+Y ∈ hδ := [h, h+δ], has a limit law fXn(x)enδ, whereψn(hδ) equals to [∂ lnP (Y ∈ yδ)/∂y]y=h plus an additional term, contributed from the correlation between Xn and bath Y . By applying this limit law to a composite heterogeneous system including a system of interest and a large but finite bath, we derive a pseudo-Hamiltonian and a corresponding generalized Boltzmann distribution law. This result is applicable to the system of arbitrary size, and also allows for strong system-bath interactions. In contrast to previous results derived with the help of an additional larger bath and a pre-determined temperature, our approach treats the composite system as an isolated system. It allows us to derive a temperature and corrections to the temperature due to the strong system-bath coupling when the bath size is not infinity. Furthermore, we discuss the thermodynamic relation of free e...
Thermodynamic laws are limiting behavior of the statistics of repeated measurements of an arbitra... more Thermodynamic laws are limiting behavior of the statistics of repeated measurements of an arbitrary system with a priori probability distribution. A duality symmetry arises, between Massieu-Guggenheim entropy and Gibbs entropy, in the limit of large number of measurements. This yields the fundamental thermodynamic relation and Hill-Gibbs-Duhem (HGD) equation as a dual pair. We show if the system itself has a second macroscopic limit that satisfies Callen's postulate that entropy being an Eulerian homogeneous function of all extensive variables, the symmetry is lost: the HGD equation reduces to the Gibbs-Duhem equation. This theory provides better logic to textbook thermodynamics, a clarification on nanothermodynamics, as well as novel ideas for a thermodynamic-like framework for single-cell biology.
In living cells, ion channels passively allow for ions to flow through as the concentration gradi... more In living cells, ion channels passively allow for ions to flow through as the concentration gradient relax to thermal equilibrium. Most ion channels are selective, only allowing one type of ion to go through while blocking another. One salient example is KcsA, which allows for larger K ions through but blocks the smaller Na ions. This counter-intuitive selectivity has been explained by two distinct theories that both focus on equilibrium properties: particle-channel affinity and particlesolvent affinity. However, ion channels operate far from equilibrium. By constructing minimal kinetic models of channels, we discover a ubiquitous kinetic ratchet effect as a non-equilibrium mechanism to explain such selectivity. We find that a multi-site channel kinetically couples the competing flows of two types of particles, where one particle’s flow could suppress or even invert the flow of another type. At the inversion point (transition between the ratchet and dud modes), the channel achieves ...
Proceedings of the National Academy of Sciences, 2017
Significance It is commonly expected that cooling a hot system takes a longer time than cooling a... more Significance It is commonly expected that cooling a hot system takes a longer time than cooling an identical system initiated at a lower temperature. Surprisingly, this is not always the case; in various systems, including water and magnetic alloys, it has been observed that a hot system can be cooled faster. These anomalous cooling effects are referred to as “the Mpemba effect”, and so far they lack a generic details-independent explanation. Based on recent developments in the theory of nonequilibrium thermodynamics, we propose a generic mechanism for similar effects, demonstrate it in various systems, and predict a similar anomalous behavior in heating. Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon—the “Mpemba effect”—was first observed in water and has recently been reported in other systems. Whereas several detail-dependent explanations were suggested for some of these observa...
Steady dissipation of energy is a crucial property that distinguishes active particles from Brown... more Steady dissipation of energy is a crucial property that distinguishes active particles from Brownian particles. However, it is not straightforward to explicitly model the dissipative property of existing active particles driven by a vibrating plate. We present a novel active particle that can be explicitly modeled by Newtonian dynamics of a conservative force field plus two asymmetrical dissipative terms. The particle is a dimer consisting of two ping-pong balls connected by a rigid rod, and its two balls are filled with granular particles of the same total mass but of different grain size. This dimer placed on a vibrating plate exhibits 3 types of motion – by tuning the frequency and the amplitude of the vibration, the dimer undergoes either a directed motion toward the small (or large) grain-filled side or an unbiased random motion. We investigate the various modes of motion both experimentally and numerically and show that the directed motion is a result of the asymmetric damping...
Statistical estimation theory determines the optimal way of estimating parameters of a fluctuatin... more Statistical estimation theory determines the optimal way of estimating parameters of a fluctuating noisy signal. However, if the estimation is performed on unreliable hardware, a sub-optimal estimation procedure can outperform the previously optimal procedure. Here, we compare classes of circadian clocks by viewing them as phase estimators for the periodic day-night light signal. We find that continuous attractor-based free running clocks, such as those found in the cyanobacterium Synechococcus elongatus and humans, are nearly optimal phase estimators since their flat attractor directions efficiently project out light intensity fluctuations due to weather patterns (`external noise'). However, such flat directions also make these continuous limit cycle attractors highly vulnerable to diffusive 'internal noise'. Given such unreliable biochemical hardware, we find that point attractor-based damped clocks, such as those found in a smaller cyanobacterium with low protein copy...
Continuous attractors have been used to understand recent neuroscience experiments where persiste... more Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions under which the emergent bump of neural activity in such networks can be manipulated by space and time-dependent external sensory or motor signals are not understood. Here, we find fundamental limits on how rapidly internal representations encoded along continuous attractors can be updated by an external signal. We apply these results to place cell networks to derive a velocity-dependent nonequilibrium memory capacity in neural networks.
Recent developments in nonequilibrium statistical mechanics suggest that the history of entropy p... more Recent developments in nonequilibrium statistical mechanics suggest that the history of entropy production in a system determines the relative likelihood of competing processes. This presents the possibility of interpreting and predicting the self-organization of complex active systems, but existing theories rely on quantities that are challenging to obtain. Here, we address this issue for a general class of Markovian systems in which two types of self-replicating molecular assemblies (self-replicators) compete for a pool of limiting resource molecules within a nonequilibrium steady state. We derive exact relations that show that the relative fitness of these species depends on a path function, ψ, which is a sum of the entropy production and a relative-entropy term. In the limit of infinite path length, ψ reduces to the entropy production. We demonstrate use of the theory by numerically studying two models inspired by biological systems, including a simplified model of a competition between strains of the yeast prion Sup35 in the presence of driven disaggregation by the ATPase Hsp104.
We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a... more We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere [1], but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of $\pi$. If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer's eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously pe...
Many organisms use free running circadian clocks to anticipate the day night cycle. However, othe... more Many organisms use free running circadian clocks to anticipate the day night cycle. However, others organisms use simple stimulus-response strategies ('hourglass clocks') and it is not clear when such strategies are sufficient or even preferable to free running clocks. Here, we find that free running clocks, such as those found in the cyanobacterium and humans, can efficiently project out light intensity fluctuations due to weather patterns ('external noise') by exploiting their limit cycle attractor. However, such limit cycles are necessarily vulnerable to 'internal noise'. Hence, at sufficiently high internal noise, point attractor-based 'hourglass' clocks, such as those found in a smaller cyanobacterium with low protein copy number, , can outperform free running clocks. By interpolating between these two regimes in a diverse range of oscillators drawn from across biology, we demonstrate biochemical clock architectures that are best suited to differ...
We extend a generalized integral fluctuation relation in diffusion processes that we obtained pre... more We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation. This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.
Proceedings of the National Academy of Sciences, 2017
Significance It is commonly expected that cooling a hot system takes a longer time than cooling a... more Significance It is commonly expected that cooling a hot system takes a longer time than cooling an identical system initiated at a lower temperature. Surprisingly, this is not always the case; in various systems, including water and magnetic alloys, it has been observed that a hot system can be cooled faster. These anomalous cooling effects are referred to as “the Mpemba effect”, and so far they lack a generic details-independent explanation. Based on recent developments in the theory of nonequilibrium thermodynamics, we propose a generic mechanism for similar effects, demonstrate it in various systems, and predict a similar anomalous behavior in heating.
land at College Park -We describe a method to compute the Helmholtz free energy of a crystalline ... more land at College Park -We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the manydimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of 10 -5 k B T per particle.
Title of dissertation: TOPICS IN EQUILIBRIUM AND NONEQUILIBRIUM THERMODYNAMICS: COMPUTING CRYSTAL... more Title of dissertation: TOPICS IN EQUILIBRIUM AND NONEQUILIBRIUM THERMODYNAMICS: COMPUTING CRYSTALLINE FREE ENERGIES AND ENGINEERING MAXWELL’S DEMON Zhiyue Lu, Doctor of Philosophy, 2015 Dissertation directed by: Professor Christopher Jarzynski Department of Chemistry and Biochemistry; Institute for Physical Science and Technology This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducin...
A simple model illustrates the operating principles of an information engine, a mechanical device... more A simple model illustrates the operating principles of an information engine, a mechanical device that mimics the behavior of Maxwell’s demon by converting heat into information plus work.
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Papers by Zhiyue Lu