arXiv subjects

Jan Korbel

Publications and source records attributed to Jan Korbel.

At least 19 recordsLinked to original sources

arXiv2026

Strengthened second law for periodic processes

Many physical systems evolve under periodic driving: the same control protocol is applied again and again, even though the state of the system itself need not return to where it started after each cycle. We derive a physics-independent lower bound on the entropy production of \emph{any} periodic process modeled by the evolution of an initial distribution $p_0$ by a repeated application of the same map $G$. This is a strict strengthening of the second law of thermodynamics for periodic processes. It does not require that the single-period dynamics arise from a CTMC, satisfy (local) detailed balance, or be subject to other typical restrictions. We discuss its application to spins in the Curie-Weiss model and Deterministic Finite Automata, with possible extensions to other uniform computers.

cond-mat.stat-mech↗

arXiv2026

Finite relaxation protocols with minimal dissipation

Work extraction from nonequilibrium systems is a major challenge across biological, chemical, physical, and engineering systems. Idealized protocols generally require a quasistatic relaxation stage in which the Hamiltonian is gradually adjusted through a continuum of intermediaries. Here, we consider protocols restricted to a finite number $N$ of intermediary Hamiltonians, consisting of a sequence of quench-relax steps. We determine the sequence of quenches that minimizes the dissipated work, which can be expressed in terms of a recurrence involving the Lambert function. The optimal sequence converges to the Fisher-Rao geodesic, saturating known leading-order dissipation bounds at large $N$. We obtain lower bounds on work extraction from a nonequilibrium distribution as a function of its Fisher-Rao distance to equilibrium. We extend and apply the framework in two simple models: (i) an optical trap experiment, showing that the optimal intermediary distribution can be bimodal even for unimodal initial and final distributions, and (ii) an enzyme-catalyzed reaction, showing that that accounting for relaxation time in addition to dissipation can favor barrier-lowering.

cond-mat.stat-mech↗

arXiv2026

Foundations of entropy in complex systems

This chapter reviews the foundations of entropy and their extensions to complex systems. We first discuss the relation between Boltzmann's formula, multiplicity, coarse-graining, and Shannon entropy, before introducing generalized entropies such as R\'enyi, Tsallis, and Burg entropy. We then examine Maxwell--Boltzmann, Bose--Einstein, and Fermi--Dirac statistics, structure-forming systems, sample-space reducing processes, P\'olya urns, and nonlinear dynamics. Axiomatic approaches are presented through the Shannon--Khinchin axioms, Tempesta group-composability, Hanel--Thurner asymptotic scaling, Shore--Johnson consistency axioms, and Lieb--Yngvason axioms. Finally, we discuss calibration invariance, Hanel--Thurner--Gell-Mann duality between linear and escort averages, and Kolmogorov--Nagumo averages, showing how the same distribution can arise from different entropies, constraints, or dynamics. These results emphasize that the choice of entropy should be guided by the structure and physical properties of the system.

cond-mat.stat-mech↗

arXiv2026

Computational foundations of the human world

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging on reliable claims. Importantly, the computational difficulty of collective decision-making, particularly the time and communication required to reach solutions, imposes fundamental constraints on social organization. While theoretical computer science offers formal tools for analyzing such problems, for instance, by analyzing resource requirements, including time and memory, surprisingly, there is no domain of social science that focuses on the nature of computation in the human world. This perspective argues that we now have the opportunity to deploy these computational frameworks to study human social organization, opening research directions at the intersection of computer science and social science. We highlight core social phenomena that can be framed as computational, including (i) distributed consensus and coordinated action, (ii) societal restructuring with scale, (iii) hierarchical and modular structure, and (iv) externalized memory systems. We identify several concepts from theoretical computer science that may provide insight into these phenomena, especially emphasizing more recently developed approaches beyond the paradigm of Turing~Machines and worst-case computational complexity.

cs.SI↗

arXiv2026

Quo vadis, stochastic thermodynamics?

Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work, heat, and entropy production to be defined along individual realizations rather than at the ensemble level only. Over the past three decades, the field has yielded fundamental results, including fluctuation theorems and several universal bounds, such as thermodynamic uncertainty relations, speed limit theorems, and many others. Many of them have been tested on a range of experimental platforms. This Perspective reviews recent developments in stochastic thermodynamics that extend its scope beyond its traditional domains, including systems with memory and hidden degrees of freedom, microscopic approaches to interacting and active matter, and geometric formulations based on optimal transport. Next, the Perspective surveys the challenges that arise when applying these ideas to macroscopic and complex systems, where the link between statistical irreversibility and thermodynamic dissipation becomes less direct. Finally, emerging applications in non-physical contexts are highlighted, including computation, biological systems, and social dynamics. Transcending the traditional boundaries of physics, these developments catalyze an unorthodox framework to tackle the thermodynamics of complex systems.

cond-mat.stat-mech↗

arXiv2025

Empirical validation of the polarization transition in a double-random field model of elections

We model bipartisan elections where voters are exposed to two forces: local homophilic interactions and external influence from two political campaigns. The model is mathematically equivalent to the random field Ising model with a bimodal field. When both parties exceed a critical campaign spending, the system undergoes a phase transition to a highly polarized state where homophilic influence becomes negligible, and election outcomes mirror the proportion of voters aligned with each campaign, independent of total spending. The model predicts a hysteresis region, where the election results are not determined by campaign spending but by incumbency. Calibrating the model with historical data from US House elections between 1980 and 2020, we find the critical campaign spending to be $\sim 1.8$ million USD. Campaigns exceeding critical expenditures increased in 2018 and 2020, suggesting a boost in political polarization.

physics.soc-ph↗

arXiv2025

What does it mean for a system to compute?

Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can identify which aspects of the dynamic system match the input and output of the computation that it performs, as well as the aspects of the dynamic system that match the intermediate logical variables of that computation. In contrast, in many naturally occurring dynamical systems that we understand to be computers, even though we neither designed nor constructed them - such as the human brain - it is not a priori clear how to identify the computation we presume to be encoded in the dynamic system. Regardless of their origin, dynamical systems capable of computation can, in principle, be mapped onto corresponding abstract computational machines that perform the same operations. In this paper, we begin by surveying a wide range of dynamic systems whose computational properties have been studied. We then introduce a very broadly applicable framework for identifying what computations(s) are emulated by a given dynamic system. After an introduction, we summarize key examples of dynamical systems whose computational properties have been studied. We then introduce a very broadly applicable framework that defines the computation performed by a given dynamical system in terms of maps between that system's evolution and the evolution of an abstract computational machine. We illustrate this framework with several examples from the literature, in particular discussing why some of those examples do not fully fall within the remit of our framework. We also briefly discuss several related issues, such as uncomputability in dynamical systems, and how to quantify the value of computation in naturally occurring computers.

physics.comp-ph↗

arXiv2025

Thermodynamics of driven systems with explicitly broken detailed balance

In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose a challenge for a consistent thermodynamic interpretation. Even steady-state potentials like entropy or free energy are no longer state variables. Here, we use a framework for systems with broken detailed balance, where Boltzmann entropy can be computed while properly taking constraints on state transitions into account. As an illustration, we establish the thermodynamic relations for arbitrarily driven sample space-reducing processes that are non-equilibrium but show steady states. We demonstrate that, despite explicitly broken detailed balance, it remains feasible to define and unambiguously interpret the effective thermodynamic potentials.

cond-mat.stat-mech↗

arXiv2023

Is stochastic thermodynamics the key to understanding the energy costs of computation?

The relationship between the thermodynamic and computational characteristics of dynamical physical systems has been a major theoretical interest since at least the 19th century, and has been of increasing practical importance as the energetic cost of digital devices has exploded over the last half century. One of the most important thermodynamic features of real-world computers is that they operate very far from thermal equilibrium, in finite time, with many quickly (co-)evolving degrees of freedom. Such computers also must almost always obey multiple physical constraints on how they work. For example, all modern digital computers are periodic processes, governed by a global clock. Another example is that many computers are modular, hierarchical systems, with strong restrictions on the connectivity of their subsystems. This properties hold both for naturally occurring computers, like brains or Eukaryotic cells, as well as digital systems. These features of real-world computers are absent in 20th century analyses of the thermodynamics of computational processes, which focused on quasi-statically slow processes. However, the field of stochastic thermodynamics has been developed in the last few decades - and it provides the formal tools for analyzing systems that have exactly these features of real-world computers. We argue here that these tools, together with other tools currently being developed in stochastic thermodynamics, may help us understand at a far deeper level just how the fundamental physical properties of dynamic systems are related to the computation that they perform.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium thermodynamics of uncertain stochastic processes

Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world experiment, there is non-zero uncertainty about the precise value of temperatures, chemical potentials, energy spectrum, etc. Here we investigate how this uncertainty modifies the theorems of stochastic thermodynamics. We consider two scenarios: in the (called \emph{effective}) scenario we fix the (unknown, randomly generated) experimental apparatus and then repeatedly observe (stochastic) trajectories of the system for that fixed apparatus. In contrast, in a (called \emph{phenomenological}) scenario the (unknown) apparatus is re-generated for each trajectory. We derive expressions for thermodynamic quantities in both scenarios. We also discuss the physical interpretation of effective (scenario) entropy production (EP), derive the effective mismatch cost, and provide a numerical analysis of the effective thermodynamics of a quantum dot implementing bit erasure with uncertain temperature. We then analyze the protocol for moving between two state distributions that maximize effective work extraction. Next, we investigate the effective thermodynamic value of information, focusing on the case where there is a delay between the initialization of the system and the start of the protocol. Finally, we derive the detailed and integrated fluctuation theorems (FTs) for the phenomenological EP. In particular, we show how the phenomenological FTs account for the fact that the longer a trajectory runs, the more information it provides concerning the precise experimental apparatus, and therefore the less EP it generates.

cond-mat.stat-mech↗

arXiv2023

Geometric Structures Induced by Deformations of the Legendre Transform

The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi's divergence and entropy in a wide range of physical phenomena. However, these early findings still provide little intuition on the nature of this relationship and its implications for physical systems. Here we shed new light on the Legendre transform by revealing the consequences of its deformation via symplectic geometry and complexification. These findings reveal a novel common framework that leads to a principled and unified understanding of physical systems that are not well-described by classic information-theoretic quantities.

cond-mat.stat-mech↗

arXiv2023

Thermodynamics of exponential Kolmogorov-Nagumo averages

This paper investigates generalized thermodynamic relationships in physical systems where relevant macroscopic variables are determined by the exponential Kolmogorov-Nagumo average. We show that while the thermodynamic entropy of such systems is naturally described by R\'{e}nyi's entropy with parameter $\gamma$, an ordinary Boltzmann distribution still describes their statistics under equilibrium thermodynamics. Our results show that systems described by exponential Kolmogorov-Nagumo averages can be interpreted as systems originally in thermal equilibrium with a heat reservoir with inverse temperature $\beta$ that are suddenly quenched to another heat reservoir with inverse temperature $\beta' = (1-\gamma)\beta$. Furthermore, we show the connection with multifractal thermodynamics. For the non-equilibrium case, we show that the dynamics of systems described by exponential Kolmogorov-Nagumo averages still observe a second law of thermodynamics and the H-theorem. We further discuss the applications of stochastic thermodynamics in those systems -- namely, the validity of fluctuation theorems -- and the connection with thermodynamic length. namic length.

cond-mat.stat-mech↗

arXiv2022

Homophily-based social group formation in a spin-glass self-assembly framework

Homophily, the tendency of humans to attract each other when sharing similar features, traits, or opinions has been identified as one of the main driving forces behind the formation of structured societies. Here we ask to what extent homophily can explain the formation of social groups, particularly their size distribution. We propose a spin-glass-inspired framework of self-assembly, where opinions are represented as multidimensional spins that dynamically self-assemble into groups; individuals within a group tend to share similar opinions (intra-group homophily), and opinions between individuals belonging to different groups tend to be different (inter-group heterophily). We compute the associated non-trivial phase diagram by solving a self-consistency equation for 'magnetization' (combined average opinion). Below a critical temperature, there exist two stable phases: one ordered with non-zero magnetization and large clusters, the other disordered with zero magnetization and no clusters. The system exhibits a first-order transition to the disordered phase. We analytically derive the group-size distribution that successfully matches empirical group-size distributions from online communities.

cond-mat.stat-mech↗

arXiv2022

Specialization in Criminal Careers

We use a comprehensive longitudinal dataset on criminal acts over five years in a European country to study specialization in criminal careers. We cluster crime categories by their relative co-occurrence within criminal careers, deriving a natural, data-based taxonomy of criminal specialization. Defining specialists as active criminals who stay within one category of offending behavior, we study their socio-demographic attributes, geographic range, and positions in their collaboration networks, relative to their generalist counterparts. In comparison to generalists, specialists tend to be older, more likely to be female, operate within a smaller geographic range, and collaborate in smaller, more tightly-knit local networks. We observe that specialists are more intensely embedded in criminal networks and find evidence that specialization indeed reflects division of labor and organization.

physics.soc-ph↗

arXiv2021

Thermodynamics of nonequilibrium systems with uncertain parameters

In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including uncertain number of heat baths / particle reservoirs, uncertainty in the precise values of temperatures / chemical potentials of those reservoirs, uncertainty in the energy spectrum, uncertainty in the control protocol, etc. We formalize such uncertainty with an (arbitrary) probability measure over all transition rate matrices satisfying local detailed balance. This lets us define the effective thermodynamic quantities by averaging over all LDB-obeying rate matrices. We show that the resultant effective entropy violates the second law of thermodynamics. In contrast to the effective entropy though, the expected stochastic entropy, defined as the ensemble average of the effective trajectory-level entropy, satisfies the second law. We then and explicitly calculate the second-order correction to the second law for the case of one heat bath with uncertain temperature. We also derive the detailed fluctuation theorem for expected effective trajectory entropy production for this case, and derive a lower bound for the associated expected work. Next, to ground these formal considerations with experimentally testable bounds on allowed energetics, we derive a bound on the maximal work that can be extracted from systems with arbitrarily uncertain temperature. We end by extending previous work on "thermodynamic value of information", to allow for uncertainty in the time-evolution of the rate matrix.

cond-mat.stat-mech↗

arXiv2021

Thermodynamics of structure-forming systems

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here we derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly captures clustered states. For large systems and low concentrations, the approach is equivalent to the grand-canonical ensemble; for small systems, we find significant deviations. We derive the detailed fluctuation theorem and Crooks' work fluctuation theorem for structure-forming systems. The connection to the theory of particle self-assembly is discussed. We apply the results to several physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phase transition.

cond-mat.stat-mech↗

arXiv2020

Balanced and fragmented phases in societies with homophily and social balance

Recent attempts to understand the origin of social fragmentation are based on spin models which include terms accounting for two social phenomena: homophily -- the tendency for people with similar opinions to establish positive relations -- and social balance -- the tendency for people to establish balanced triadic relations. Spins represent attribute vectors that encode multiple (binary) opinions of individuals and social interactions between individuals can be positive or negative. Recent work suggests that large systems of N >> 1 individuals never reach a balanced state (where unbalanced triads with one or three hostile links remain), provided the number of attributes for each agent is less than O(N^2) [Phys. Rev. Lett. 125, 078302]. Here we show that this statement is overly restrictive. Within a Hamiltonian framework that minimizes individuals' social stress, we demonstrate that stationary, balanced, but fragmented states can be reached for any number of attributes, if, in addition to homophily, individuals take into account a significant fraction, q, of their triadic relations. Above a critical value q_c, balanced states result. This result also holds for sparse realistic social networks. Finally, in the limit of small q, our result agrees with that of [Phys. Rev. Lett. 125, 078302].

physics.soc-ph↗

arXiv2020

Stochastic thermodynamics and fluctuation theorems for non-linear systems

We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when those assumptions are relaxed, then it cannot be formulated in terms of Shannon entropy. However, thermodynamic consistency is salvaged if we reformulate the second law in terms of generalized entropy; our first result is an equation relating the precise form of the non-linear master equation to the precise associated generalized entropy which results in thermodynamic consistency. We then build on this result to extend the usual trajectory-level definitions of thermodynamic quantities that are appropriate even when the two assumptions are relaxed. We end by using these trajectory-level definitions to derive extended versions of the Crooks fluctuation theorem and Jarzynski equality which apply when the two assumptions are relaxed.

cond-mat.stat-mech↗