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Quo vadis,

stochastic thermodynamics?

Jan Korbel

Complexity Science Hub

CCS 2026 satellite session

Thriving in the Extremes

The paper behind this talk

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Quo vadis, stochastic thermodynamics?

With my co-authors

Artemy

Kolchinsky

Sarah A. M.

Loos

Gonzalo

Manzano

Rosalba

Garcia-Millan

Olga Movilla

Miangolarra

Édgar

Roldán

Journal of Non-Equilibrium Thermodynamics

doi.org/10.1515/jnet-2026-0051

Portraits: SFI, APS Physics, Google Scholar, King's College London, UC Irvine and ICTP public profiles.

Thirty years of stochastic thermodynamics

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1990s

Foundations

• Stochastic energetics

• Fluctuation theorems

• Jarzynski–Crooks relations

2000s

Trajectory theory

• Entropy production

• Information thermodynamics

• Feedback and response

2010s

Universal bounds

• Uncertainty relations

• Speed-limit theorems

• First-passage statistics

Today

New regimes

• Hidden variables & memory

• Active & interacting matter

• Optimal transport & scaling

The original dream

A tiny machine converts fuel and information into useful work while dissipating heat along a fluctuating trajectory.

Success at small scales created today’s scaling questions.

Figure: Korbel et al. (2026), Fig. 1. Timeline synthesized from Sections 1 and 6.

Thermodynamics along individual trajectories

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A stochastic path and the experiment played backward

Forward path γ

Reversed path γ̄

† means the reversed dynamics—and the reversed driving protocol when present.

What the equation compares

Probability of the observed forward trajectory

Probability under the physically reversed experiment

Local detailed balance

connects a transition-rate ratio to environmental entropy

Irreversibility is forward–reverse distinguishability. With complete microscopic dynamics and local detailed balance, it equals total entropy production divided by kᴮ.

Figure: Cao & Liang, Quantitative Biology 13, e75, doi:10.1002/qub2.75, Fig. 2. Relation: Korbel et al. (2026); Seifert (2005).

Microscopic foundations of stochastic thermodynamics

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At small scales, thermal fluctuations are comparable to internal energy changes

What microscopic resolution provides

Trajectory thermodynamics

Work, heat and entropy production can be assigned to each fluctuating realization, rather than only to an ensemble average.

Physical interpretation

Resolved states, transition rates and reservoirs let local detailed balance connect time asymmetry to dissipated heat.

Predictive constraints

Fluctuation theorems and universal tradeoffs constrain accuracy, current fluctuations and transformation speed.

Microscopic example: Hopfield–Ninio kinetic proofreading

One driven proofreading stage doubles the discrimination exponent in the ideal limit. The gain requires chemical work, and approaching the error limit slows product formation.

Figure: Cao & Liang (2025), Fig. 5; Hopfield (1974). Context: Korbel et al. (2026), Sections 1 and 5.

Optimal transport and finite-time dissipation

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Moving probability farther and faster requires more dissipation

Redistributing probability

The initial distribution p₀ must be transported to pτ within the available time τ.

Wasserstein–2 transport cost

W₂ is the minimum quadratic cost of coupling the initial and final probability distributions.

Finite-time lower bound

overdamped Langevin dynamics with constant diffusivity D

What optimal transport adds

The bound quantifies the unavoidable cost. The minimizing probability flow also identifies the least-dissipative protocol within the specified dynamical model.

Near equilibrium, Fisher geometry and thermodynamic length play the analogous role. Beyond overdamped diffusion, the appropriate transport geometry is not unique.

Korbel et al. (2026), Section 4; Aurell et al., J. Stat. Phys. 147, 487–505 (2012); Shiraishi et al., PRL 121, 070601 (2018).

Several geometries of dissipation

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Different dynamics induce different notions of distance and thermodynamic length

Near equilibrium

Overdamped diffusion

Beyond overdamped

Fisher metric

Thermodynamic length

Controls excess dissipation for slow driving close to equilibrium.

Wasserstein–2

Quadratic transport length

The geodesic probability flow minimizes finite-time dissipation for overdamped Langevin dynamics.

Generalized transport

Wasserstein–1 and other costs

Jump processes, reaction networks and constrained dynamics can require a different cost and therefore a different geometry.

There is no universal thermodynamic metric: the dynamics determine the geometry.

Korbel et al. (2026), Sec. 4; Crooks (2007); Aurell et al. (2012).

Hidden variables create memory

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A Markov process can look non-Markovian when its state is only partially observed

Why memory appears

The hidden state xₖ is Markovian.

The observation yₖ is noisy and incomplete.

Past observations help infer the current hidden state.

Observed irreversibility is a lower bound on the full entropy production

Equality requires local detailed balance and a complete thermodynamic state.

Approaches to hidden Markovian systems

infer lower bounds from partial time series

embed the dynamics in an enlarged Markovian state

formulate non-Markovian thermodynamics directly

Figure: Bechhoefer, New J. Phys. 17, 075003 (2015), Fig. 4. Framework: Korbel et al. (2026), Section 2.

Active and interacting matter

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Energy-consuming agents generate probability currents across scales

Key highlights from the Perspective

Currents are the signature

Fuel-driven currents reveal broken time reversal and may organize collective circulation.

Irreversibility is many-body

Doi–Peliti and Dean field theories retain interactions and multiplicative noise. Short-time terms set the rate.

A microscopic correlation rule

Pair interactions require three-point correlations. Short-range forces can reduce this to two-point form.

In the published figure, cycles in strain space yield probability currents and spatial maps of partial entropy production.

Figure: Tan et al., Nature 607, 287–293 (2022), Fig. 4. Framework: Korbel et al. (2026), Section 3.

The scaling wall

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Microscopic scale

Local detailed balance links statistical asymmetry to physical dissipation

After coarse-graining

Hidden pathways are merged: data processing preserves only a lower bound, which can become extremely loose

Single transition

ATP hydrolysis

ΔSₑₙᵥ/kᴮ ≈ 10 to 20

Glucose oxidation

ΔSₑₙᵥ/kᴮ ≈ 1.2 × 10³

Coarse-grained observation

cytoskeleton

underestimate ≈ 10⁶

brain dynamics

underestimate > 10²⁰

Entropy production: physical cost requiring energies, reservoirs and local detailed balance

Irreversibility: forward–reverse distinguishability for any time series

Korbel et al. (2026), Section 5; Foster et al., PNAS 120 (2023); Lynn et al., PNAS 118 (2021).

A careful bridge to Active Inference

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An extension of the Perspective: connecting statistical boundaries with thermodynamic interpretation

Definition

Internal states μ and external states η become conditionally independent when the blanket B, formed by sensory states s and active states a, is known.

External world

η

Blanket B

Sensory s

retinal signals

Active a

muscle activity

Internal μ

neural states

→

→

←

←

observations

actions

Relation to stochastic thermodynamics

The blanket trajectory exposes only part of the full dynamics. Marginalizing hidden variables can only reduce measured time irreversibility.

Example: an embodied agent samples the external world through retinal signals and changes it through muscle activity; its neural states remain behind the blanket.

The inequality becomes a statement about physical dissipation only when a model identifies energies and reservoirs and satisfies local detailed balance.

Conditional independence specifies a boundary; energies, reservoirs and local detailed balance specify thermodynamics.

Markov-blanket definition: Parr, Da Costa & Friston, Phil. Trans. R. Soc. A 378, 20190159 (2020). Thermodynamic bound: Korbel et al. (2026), Sections 2 and 5.

Irreversibility beyond energetic models

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Forward–reverse asymmetry remains measurable even when no physical energy bookkeeping is available

Social dynamics

Opinion formation, imitation and collective decisions can show directional cycles and broken time-reversal symmetry.

Role: diagnose directional collective organization

Abstract computation

Logical or algorithmic state transitions have path probabilities, activity and timing—even before a hardware energy model is specified.

Role: formulate tradeoffs in information, time and activity

Biological & neural data

Brain states, disease markers and intracellular regulation can be classified by their degree and structure of time asymmetry.

Role: infer hidden nonequilibrium organization from data

What survives from stochastic thermodynamics

path probabilities · fluctuation relations · inference bounds · generalized resource tradeoffs

Without energies, reservoirs and local detailed balance, irreversibility is not a physical dissipation rate.

Korbel et al. (2026), Section 5 and outlook; statistical irreversibility is used here independently of an energetic interpretation.

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Limits define the frontier

Stochastic thermodynamics is becoming a framework for irreversibility, constraints and tradeoffs in complex systems.

Which thermodynamic structures survive coarse-graining?

Questions